Fractal Geometry and Spatial Phenomena

A Bibliography

January 1991

Mark MacLennan, A. Stewart Fotheringham, and Michael Batty

NCGIADepartment of Geography

State University at BuffaloBuffalo, NY 14261

Paul A. Longley

Wales and South West England Regional Research LaboratoryUniversity of WalesCardiff CF1 3YN

National Center for Geographic Information and Analysis

Report 91-1

- 2 -

TABLE OF CONTENTS

PREFACE ......................................................................................... 3

I. GENERAL REFERENCES ......................................................... 4I.1 TEXTS ................................................................................. 4I.2 JOURNAL ARTICLES .............................................................. 5

II. MEASUREMENT ISSUES........................................................... 8II.1 ESTIMATION OF FRACTAL DIMENSION - GENERAL ISSUES .......... 8II.2 ESTIMATION OF FRACTAL DIMENSION FOR CURVES/PROFILES ... 9II.3 ESTIMATION OF FRACTAL DIMENSION FOR SURFACES ............... 10II.4 SPACE FILLING CURVES ......................................................... 11

III APPLICATIONS ...................................................................... 13III.1 CARTOGRAPHIC GENERALIZATION .......................................... 13III.2 LENGTH ESTIMATES AND SELF-SIMILIARITY OF LINES ............... 14III.3 VISUAL PERCEPTION .............................................................. 15III.4 TERRAIN CHARACTERIZATION ................................................ 16III.5 METEOROLOGY ...................................................................... 20III.6 OCEANOGRAPHY ................................................................... 22III.7 GEOMORPHOLOGY/HYDROLOGY .............................................. 24III.8 HYDRAULICS AND FLUID MECHANICS ...................................... 28III.9 EARTH SCIENCES ................................................................... 28III.10 ECOLOGY/LANDSCAPE ............................................................ 34III.11 URBAN STRUCTURES ............................................................. 36III.12 HUMAN GEOGRAPHY............................................................... 37III.13 REMOTE SENSING .................................................................. 37III.14 IMAGE COMPRESSION ............................................................ 38III.15 IMAGE PROCESSING ............................................................... 40III.16 FRACTAL SYNTHESIS ............................................................. 44

IV. MISCELLANEOUS.................................................................... 47

- 3 -

PREFACE

Fractal research seems to have permeated most, if not all, areas of research concerned withform, from the micro-level aggregation of water molecules or particles of zinc oxide to themacro analysis of the structure of landmasses and cities. Given that the study of spatialform and its links to spatial processes is one of basic research areas within Geography, itis not surprising that research on fractals can be found in many subfields of the discipline,including geomorphology, climatology, urban and regional analysis, cartography, andremote sensing.

Within this working paper, we provide a sample of the growing literature in this area. Theemphasis is on references that have appeared in the published literature. The bibliographyis arranged in three sections: general references; measurement issues; and applications.Each of these general topics is further subdivided. While we have attempted to be asconsistent as possible in our indexing, there are many references that could be placed inmore than one category and in some cases the decision into which category they are placedhas been somewhat subjective. To minimize this problem, in some cases where areference clearly spans two or more of our subheadings, we have listed the reference morethan once. Additional references of interest but which do not fall into any of thedesignated categories are listed at the end of this bibliography under the heading ofmiscellaneous.

The concepts associated with fractal analysis have been discussed at the SpecialistMeetings of Initiatives 1 (The Accuracy of Spatial Data) and 3 (Multiple Representations)and we acknowledge these meetings as a source of inspiration for the development of thisbibliography. We would also like to acknowledge the financial support of the NationalCenter for Geographic Information and Analysis under NSF grant (SES-8810917).

- 4 -

I. GENERAL REFERENCES

I.1 TEXTS

Aharony, A., and J. Feder, editors, (1990) Fractals in Physics. North-Holland,Amsterdam.

Barnsley, M. F. (1988) Fractals Everywhere. Academic Press, New York.

Barnsley, M. F., and A.D. Sloan, editors, (1986) Chaotic Dynamics and Fractals.Academic Press, New York.

Briggs, J., and F. D. Peat (1990) Turbulent Mirror: an Illustrated Guide to ChaosTheory and the Science of Wholeness. Harper and Row, New York.

Davies, P. (1989) The New Physics. Cambridge University Press, Cambridge.

Devaney, R. (1989) Chaos, Fractals & Dynamics. Addison-Wesley, Reading,Massachusetts.

Falconer, K. J. (1985) The Geometry of Fractal Sets. Cambridge University Press,Cambridge.

Falconer, K. J. (1990) Fractal Geometry. John Wiley & Sons, New York.

Feder, J. (1988) Fractals. Plenum, New York.

Fischer, P., and W. R. Smith, editors, (1985) Chaos, Fractals and Dynamics. MarcelDekker, New York.

Fleischmann, M., D. J. Tildesley, and R.C. Ball, editors, (1989) Fractals in the NaturalSciences. Princeton University Press, Princeton, New Jersey.

Hideki, T. (1990) Fractals in the Physical Sciences. St. Martin's Press, New York.

Holden, A. V., editor, (1986) Chaos. Manchester University Press and Princeton UniversityPress, Princeton, New Jersey.

Jullien, R., and R. Botet (1986) Aggregation and Fractal Aggregates, WorldScientific, Singapore.

Kachigan, S.K. (1991) The Fractal Notion: A Modern Analytical Tool. RadiusPress, New York.

Kaye, B. H. (1989) A Random Walk Through Fractal Dimensions. VCH, NewYork.

Mandelbrot, B. B. (1975) Les Objets Fractals: Forme, Hasard et Dimension.Flammarion, Paris.

Mandelbrot, B. B. (1977) Fractals: Form, Chance and Dimension. W.H. Freeman,San Francisco.

- 5 -

Mandelbrot, B. B. (1983) The Fractal Geometry of Nature. 3rd Edition. W.H.Freeman, San Francisco.

Peitgen, H.-O., and D. Saupe, editors, (1988) The Science of Fractals. Springer-Verlag,New York.

Peitgen, H.-O., and P. H. Richter (1986) The Beauty of Fractals. Springer-Verlag, NewYork.

Pickover, C. A. (1990) Computers, Pattern, Chaos and Beauty: Graphics From anUnseen World. St. Martin's Press, New York.

Pietronero, L., editor, (1990) Fractals: Physical Origin and Properties. PlenumPress, New York.

Pietronero, L., and E. Tosatti, editors, (1986) Fractals in Physics. North-Holland,Amsterdam.

Sholz, C. H., and B. B. Mandelbrot, editors, (1989) Fractals in Geophysics. BirkhäuserVerlag, Basel.

Stevens, R. T. (1989) Fractal Programming in C. M&T Books, Redwood City,California.

Stevens, R.T. (1990) Advanced Fractal Programming. M&T Books, Redwood City,California.

Stevens, R.T. (1990) Fractal Programming and Ray Tracing with C++. M&TBooks, Redwood City, California.

Stevens, R.T. (1990) Fractal Programming in Turbo Pascal. M&T Books, RedwoodCity, California.

Takayasu, H. (1990) Fractals in the Physical Sciences. Manchester University Press,Manchester.

Vicsek, T. (1988) Fractal Growth Phenomena. World Scientific, Singapore.

I.2 JOURNAL ARTICLES

Bak, P., and K. Chen (1989) The physics of fractals, Physica D, 38(1), 5-12.

Barcellos, A. (1984) Additional perspectives on fractals, The College MathematicsJournal, 15(2), 115-119.

Barcellos, A. (1984) The fractal dimension of Mandelbrot, The College MathematicsJournal, 15(2), 98-114.

- 6 -

Batty, M. (1985) Fractals - geometry between dimensions, New Scientist, 105(1540), 31-35.

Batty, M. (1985) Questa montagna che non finisce mai, Genius, 10, 26-34.

Batty, M. (1989) Geography and the new geometry, Geography Review, 2(4), 7-10.

Berry, M. V., and Z. V. Lewis (1980) On the Weierstrass-Mandelbrot fractal function,Proceedings of the Royal Society of London, Series A, 370, 459-484.

Bookstein, F. L. (1977) The study of shape transformation after D'Arcy Thompson,Mathematical Biosciences, 34, 177-219.

Domb, C. (1989) Of men and ideas (After Mandelbrot), Physica D, 38(1), 64-70.

Dyson, F. (1978) Characterizing irregularity, Science, 200, 677-678.

Fotheringham, A. S. What's the fuss about fractals? (1990) Environment and PlanningA, 22(6), 716-718.

Goodchild, M. F. (1980) Fractals and the accuracy of geographical measures, MathematicalGeology, 12(2), 85-98.

Goodchild, M. F., and D. M. Mark (1987) The fractal nature of geographic phenomena,Annals of the Association of American Geographers, 77(2), 265-278.

Hutchinson, J. (1981) Fractals and self-similarity, Indiana University MathematicsJournal, 30(5), 713-747.

Jügens, H., H.-O. Peitgen, and D. Saupe (1990) The language of fractals, ScientificAmerican, 262(8), 60-67.

Kadanoff, L. P. (1986) Fractals - where's the physics? Physics Today, 39(2), 6-7.

Kolata, G. (1984) Esoteric math has practical result, Science, 225, 494-495.

Krantz, S. G. (1989) Fractal geometry, The Mathematical Intelligencer, 11(4), 12-16.

La Brecque, M. (1985) Fractal symmetry, Mosaic, 16(1), 10-23.

La Brecque, M. (1986/7) Fractal applications, Mosaic, 17(4), 34-48.

La Brecque, M. (1987) Fractals in physics, Mosaic, 18(2), 22-37.

Maddox, J. (1986) Gentle warning on fractal fashions, Nature, 322, 303.

Mandelbrot, B. B. (1978) The Fractal geometry of trees and other natural phenomena, inLecture Notes in Biomathematics, 23, Springer-Verlag, New York, 235-249.

Mandelbrot, B. B. (1981) Scalebound or scaling shapes: A useful distinction in the visual artsand in the natural sciences, Leonardo, 14(1), 45-47.

- 7 -

Mandelbrot, B. B. (1982) The many faces of scaling: fractals, geometry of nature, andeconomics, in Self-Organization and Dissipative Structures, W. C. Shieve andP. M. Allen, editors, University of Texas Press, Austin, 91-109.

Mandelbrot, B. B. (1983) On fractal geometry, and a few of the mathematical questions it has raised,Proceedings of the International Congress of Mathematicians, August 16-24,Warsaw, 1661-1675.

Mandelbrot, B. B. (1984) Fractals in physics: squig clusters, diffusions, fractal measures, andthe unicity of fractal dimensionality, Journal of Statistical Physics, 34:(5/6), 895-929.

Mandelbrot, B. B. (1985) Self-affine fractals and fractal dimension, Physica Scripta,32(4), 257-260.

Mandelbrot, B. B. (1986) Self-affine fractal sets, I: The basic fractal dimensions, in Fractalsin Physics, L. Pietronero and E. Tosatti, editors, North-Holland, New York, 3-15.

Mandelbrot, B. B. (1986) Self-affine fractal sets, II: Length and surface dimensions, inFractals in Physics, L. Pietronero and E. Tosatti, editors, North-Holland, N.Y., 17-20.

Mandelbrot, B. B. (1986) Self-affine fractal sets, III: Hausdorff dimension anomalies andtheir implications in Fractals in Physics, L. Pietronero and E. Tosatti, editors, North-Holland, N.Y., 21-28.

Mandelbrot, B. B. (1989) Fractal geometry - what is it, and what does it do, Proceedingsof the Royal Society of London, Series A, 423(1864), 3-16.

Mandelbrot, B. B. (1989) Fractals and an art for the sake of science, Leonardo, ComputerArt in Context Supplemental Issue, 21-24.

Mandelbrot, B. B. (1989) Some 'facts' that evaporate upon examination, The MathematicalIntelligencer, 11(4), 17-19.

Mandelbrot, B. B., and J. W. Van Ness. (1968) Fractional brownian motions, fractionalnoises and applications, SIAM Review, 10(4), 422-437.

Mandelbrot, B. B., and R. F. Voss (1983) Why is nature fractal and when should noises bescaling?, in Noise in Physical Systems and 1/f Noise, M. Savelli, G. Lecoy andJ.-P. Nougier, editors, Elsevier, New York, 31-39.

McDermott, J. (1983) Geometrical forms known as fractals find sense in chaos,Smithsonian, December, 110-117.

Mecholsky, J. J. (1986) Fractals - fact or fiction? Earth and Mineral Sciences, 55(3),29-33.

Peterson, I. (1984) Ants in labyrinths and other fractal excursions, Science News, 125(Jan.21), 42-43.

Pool, R. (1990) Fractal fracas, Science, 249, 363-364.

- 8 -

Ralston, A. (1986) Discrete mathematics: the new mathematics of science, AmericanScientist, 74, 611-618.

Schechter, B. (1982) A new geometry of nature, Discover, June, 66-68.

Sapoval, B. (1987) Natural processes and fractal geometry, Acta Stereologica, 6,supplement 3, parts 1-2, 785-798.

Schroeder, M. R. (1989) Self-similarity and fractals in science and art, Journal of theAudio Engineering Society, 37(10), 795-808.

Unwin, D. (1989) Fractals and the geosciences: Introduction, Computers & Geosciences,15(2), 163-166.

Voss, R. F. (1989) Random fractals: Self-affinity in noise, music, mountains, and clouds,Physica D, 38, 362-371.

West, B. J., and M. Shlesinger (1990) The noise in natural phenomena, AmericanScientist, 78(Jan./Feb.), 40-45.

Wilson, K. G. (1987) Problems in physics with many scales of length, ScientificAmerican, 241(2), 140-157.

II. MEASUREMENT ISSUES

II.1 ESTIMATION OF FRACTAL DIMENSION - GENERAL ISSUES

Fox, C. G. (1989) Empirically derived relationships between fractal dimension and power lawfrequency spectra, Pure and Applied Geophysics, 131(1/2), 1-29.

Giorgilli, A., D. Casati, L. Galgani, and L. Sironi (1986) An efficient procedure to computefractal dimesions by box counting, Physics Letters A, 115(5), 202-206.

Halsey, T. C., M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman (1986)Fractal measures and their singularities: The characterization of strange sets, PhysicalReview A, 33(2), 1141-1151.

Hunt, F., and F. Sullivan (1986) Efficient algorithms for computing fractal dimensions, inSynergetics, G. Mayer-Kress, editor, Springer Series, 32, Springer-Verlag, NewYork, 74-81.

Liebovitch, L. S., and T. Toth (1989) A fast algorithm to determine fractal dimensions by boxcounting, Physics Letters A, 141(8/9), 386-390.

Maragos, P., and F. K. Sun (1989) Measuring fractal dimension - morphological estimatesand iterative optimization, Visual Communications and Image Processing,Proceedings of SPIE, 1199, Nov. 8-10, Philadelphia, 416-430.

- 9 -

Saupe, D. (1988) Algorithms for random fractals, in The Science of Fractal Images, H.-O. Peitgen and D. Saupe, editors, Springer-Verlag, New York, 71-136.

Stein, M. C., and K. D. Hartt (1988) Nonparametric-estimation of fractal dimension, VisualCommunications and Image Processing'88, Proceedings of SPIE, 1001, 132-137.

Taylor, C. C. (1987) Estimating fractal dimension, Acta Stereologica, 6, supplement 3,parts 1-2, 851-854.

Tél, T., A. Fülöp, and T. Vicsek (1989) Determination of fractal dimensions for geometricalmultifractals, Physics A, 159, 155-166.

Theiler, J. (1990) Estimating fractal dimension, Journal of the Optical Society ofAmerica A - Optics and Image Science, 7(6), 1055-1073.

Vepsalainen, A. M., and J. Ma (1989) Estimating of fractal dimension and correlationdimension from 2D-images and 3D-images, Visual Communications and ImageProcessing, Proceedings of SPIE, 1199, Nov. 8-10, Philadelphia, 431-439.

Voss, R. F (1986) Random fractals: characterization and measurement, Physica Scripta,33, 27-32.

Voss, R. F. (1988) Fractals in nature: From characterization to simulation, in The Scienceof Fractal Images, H.-O. Peitgen and D. Saupe, editors, Springer-Verlag, New York,21-70.

II.2 ESTIMATION OF FRACTAL DIMENSION FOR CURVES/PROFILES

Clark, N. N. (1986) Fractal harmonics and rugged materials, Nature, 319, 6052.

Clark, N. N. (1986) Three techniques for implementing digital fractal analysis of particleshape, Powder Technology, 46, 45-52.

Creutzburg, R., and E. Ivanov (1989) Fast algorithm for computing fractal dimensions ofimage segments, in Recent Issues in Pattern Analysis and Recognition, V.Cantoni, R. Creutzburg, S. Levialdi and G. Wolf, editors, Lecture Notes in ComputerScience, 399, Springer-Velag, New York, 42-51.

Dubuc, B., J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker (1989)Evaluating the fractal dimension of profiles, Physical Review A, 39(3), 1500-1512.

Gagnepain, J. J., and C. Roques-Carmes (1986) Fractal approach to two-dimensional andthree-dimensional surface roughness, Wear, 109(1/4), 119-126.

Kennedy, S. K., and W.-H. Lin (1986) FRACT - A fortran subroutine to calculate thevariables necessary to determine the fractal dimension of closed forms, Computers &Geosciences, 12(5), 705-712.

- 10 -

Longley, P. A., and M. Batty (1989) Fractal measurement and line generalization,Computers and Geosciences, 15(2), 167-183.

Longley, P. A., and M. Batty (1989) Measuring and simulating the structure and form ofcartographic lines, in J. Hauer, H. Timmermans, and N. Wrigley, editors, UrbanDynamics and Choice Behaviour, Kluwer, New York, 269-292.

Longley, P. A., and M. Batty (1989) On the fractal measurement of geographical boundaries,Geographical Analysis, 21(1), 47-67.

Matsushita, M., and S. Ouchi (1989) On the self-similarity of various curves, Physica D,38, 246-251.

Malinverno, A. (1990) A simple method to estimate the fractal dimension of self-affine series,Geophysical Research Letters, 17(11), 1953-1956.

Peleg, M., and M. D. Normand (1985) Mechanical stability as the limit to the fractaldimension of solid particle silhouettes, Powder Technology, 43, 187-188.

Pickover, C. A. (1986) A Monte Carlo approach for Epsilon placement in fractal-dimensioncalculations for waveform graphs, Computer Graphics Forum, 5, 203-210.

Richter, P. H., and H. Peitgen (1985) Morphology of complex boundaries, BerichteBunsengesellschaft fuer Physikalische Chemie, 89(6), 571-588.

Schwarz, H., and H. E. Exner (1980) The implementation of the concept of fractal dimensionon a semi-automatic image analyser, Powder Technology, 27, 207-213.

Shelberg, M. C., H. Moellering, and N. Lam (1982) Measuring the fractal dimensions ofempirical cartographic curves, Proceedings, Fifth International Symposium onComputer-Assisted Cartography (AUTO-CARTO 5), August 22-28, CrystalCity, Virginia, 481-490.

II.3 ESTIMATION OF FRACTAL DIMENSION FOR SURFACES

Clarke, K. C. (1986) Computation of the fractal dimension of topographic surfaces using thetriangular prism surface area method, Computers & Geosciences, 12(5), 713-722.

Dubuc, B., C. Roquescarmes, C. Tricot, and S.W. Zucker (1987) The variation method - Atechnique to estimate the fractal dimension of surfaces, Visual Communications andImage Processing II, Proceedings of SPIE, 845, Oct. 27-29, Cambridge,Massachusetts, 241-248.

Dubuc, B., S. W. Zucker, C. Tricot, J. F. Quinou, and D. Wehbi (1989) Evaluating the fractaldimension of surfaces, Proceedings of the Royal Society of London A,425(1868), 113-127.

Gårding, J. (1988) Properties of fractal intensity surfaces, Pattern Recognition Letters,8(5), 319-324.

- 11 -

Hayward, J., J. D. Orford, and W. B. Whalley (1989) Three implementations of fractalanalysis of particle outlines, Computers and Geosciences, 15(2), 199-207.

Hough, S. E. (1989) On the use of spectal methods for the determination of fractal dimension,Geophysical Research Letters, 16(7), 673-676.

Paumgartner, D., G. Losa, and E. R. Weibel (1981) Resolution effect on the stereologicalestimation of surface and volume and its interpretation in terms of fractal dimensions,Journal of Microscopy, 121(1) 51-63.

Sayles, R. S., and T. R. Thomas (1978) Topography of random surfaces, Nature, 273, 573.

Shelberg, M. C., and H. Moellering (1983) IFAS: A program to measure fractal dimensionsof curves and surfaces, Proceedings, ACSM-ASP Technical Meeting,Washington, D.C., 483-492.

Shelberg, M. C., H. Moellering, and N. Lam (1983) Measuring the fractal dimensions ofsurfaces, Proceedings, Sixth International Symposium on AutomatedCartography (AUTO-CARTO 6), 2, Oct. 16-21, Ottawa, 319-328.

II.4 SPACE FILLING CURVES

Abel, D.J. and D.M. Mark (1990) A comparative analysis of some two-dimensional orderings,International Journal of Geographical Information Systems, 4(1), 21-32.

Butz, A. R. (1969) Convergence with Hilbert's space filling curve, Journal of ComputingScience, 3(5), 128-146.

Butz, A.R. (1971) Alternative algorithms for Hilbert's space-filling curve, IEEETransactions on Computers, 20:4, 424-426.

Cole, A. J. (1983) A note on space filling curves, Software Practice and Experience,13, 1181-1184.

Cole, A. J. (1985) A note on Peano polygons and gray codes, International Journal ofComputer Mathematics, 18, 3-13.

Cole, A. J. (1987) Compaction techniques for raster scan graphics using space-filling curves,The Computer Journal, 30(1), 87-92.

Davies, I. M. (1987) Space filling curves and fractals on micros, The Institute ofMathematics and its Applications, 23, 94-99.

Fisher, A. J. (1986) A new algorithm for generating Hilbert curves, Software Practice andExperience, 16, 5-12.

Goldschlager, L. M. (1981) Short algorithms for space filling curves, Software Practiceand Experience, 11(1), 99-100.

- 12 -

Goodchild, M. F., and A. W. Grandfield (1983) Optimizing raster storage: An examination offour alternatives, Proceedings, Sixth International Symposium on AutomatedCartography (AUTO-CARTO 6), 1, Oct. 16-21, Ottawa, 400-407.

Griffiths, J. G. (1985) Table-driven algorithms for generating space-filling curves,Computer Aided Design, 17(1), 37-41.

Holbrook, J. A. R. (1981) Stochastic independence and space-filling curves, AmericanMathematical Monthly, June/July, 426-432.

Laurini, R. (1985) Graphics databases built on peano space-filling curves, Proceedings ofthe Eurographics'85 Conference, September 8-13, Nice, France, 327-338.

Laurini, R., and F. Milleret (1987) Les relations de Peano dans les bases de donnéesgéographiques, Symposium Proceedings, Geomatics Applied to MunicipalManagement, Nov. 4-6, Montreal, Quebec, 65-78.

Mark, D. M., and M. F. Goodchild (1986) On the ordering of two-dimensional space:Introduction & relation to tesseral principles, in Spatial Data Processing UsingTesseral Methods: Collected Papers from Tesseral Workshops 1 and 2, B.Diaz and S. Bell,editors, NERC Unit for Thematic Information Systems, Reading, U.K.,179-192.

Matias, Y., and A. Shamir (1988) A video scambling technique based on space filling curves,Lecture Notes in Comptuer Science, 293, 398-417.

Medioni, G., and Y. Yasumoto (1984) A Note on using the fractal dimension forsegmentation, Proceedings of the Workshop on Computer VisionRepresentation and Control, April 30-May 2, Annapolis, Maryland, 5-30.

Nguyen, P. T., and J. Quinqueton (1982) Space filling curves and texture analysis,Proceedings, Sixth International Conference on Pattern Recognition, Oct.19-22, Munich, Germany, 282-285.

Null, A. (1971) Space-filling curves, or how to waste time with a plotter, SoftwarePractice and Experience, 1, 403-410.

Palmer, J. A. B. (1986) A Fortran procedure for drawing some space-filling curves,Software Practice and Experience, 16, 559-574.

Patrick, E. A., D. R. Anderson and F. K. Bechtel (1968) Mapping multi-dimensional space toone dimension for computer output display, IEEE Transactions on Computers,17(10), 949-953.

Pendock, N. (1985) Fast classification of image data with large spectral dimension,Proceedings, Nineteenth International Symposium on Remote Sensing ofEnvironment, Oct. 21-25, Ann Arbor, Michigan, 281-285.

Platzman, L. K., and J. J. Bartholdi III (1986) Routing and scheduling algorithms based onspacefilling Curves, Proceedings, IEEE International Conference on Systems,Man, and Cybernetics, II, Oct. 14-17, Atlanta, Georgia, 1292-1293.

- 13 -

Platzman, L. K., and J. J. Bartholdi III (1989) Spacefilling curves and the planar travellingsalesman problem, Journal of the Association for Computing Machinery,36(4), 719-737.

Simon, J. C., and J. Quinqueton (1980) On the use of a peano scanning in image processing,in Issues in Digital Image Processing, in R.M. Haralick and J.C. Simon, editors,Sijthoff & Noordhoff, Germantown, Maryland, 357-366.

Stevens, R. J., A. F. Lehar, and F. H. Preston (1983) Manipulation and presentation ofmultidimension Data using the Peano scan, IEEE Transactions on Pattern Analysisand Machine Intelligence, 5(5), 520-526.

Wang, C.Y., and J.B. Bassingthwaighte (1990) Area-filling distributive network model,Mathematical Computer Modelling, 13(10), 27-33.

Witten, I. H., and B. Wyvill (1983) On the generation and use of space filling curves,Software Practice and Experience, 13(6), 519-525.

Yang, K.-M., L. Wu, and M. Mills (1988) Fractal based coding scheme using Peano scan,Proceedings, IEEE International Symposium on Circuits and Systems, June7-9, Espoo, Finland, 2301-2304.

III. APPLICATIONS

III.1 CARTOGRAPHIC GENERALIZATION

Armstrong, M. P., and L. D. Hopkins (1983) Fractal enhancement for thematic display oftopologically stored data, Proceedings, Sixth International Symposium onAutomated Cartography (AUTO-CARTO 6), 2, Oct. 16-21, Ottawa, 309-318.

Butttenfield, B. P. (1984) Line Structure in Graphic and Geographic Space.Unpublished PhD, Department of Geography, University of Washington, Seattle.

Buttenfield, B. P. (1986) Digital definitions of scale-dependent line structure, Proceedings,AUTO-CARTO LONDON, 1, September 14-19, London, 497-506.

Buttenfield, B. P. (1989) Scale-dependence and self-similarity in cartographic lines,Cartographica, 26(1), 79-100.

Carstensen Jr., L. W. (1989) A fractal analysis of cartographic generalization, TheAmerican Cartographer, 16(3), 181-189.

Dell'Orco, P., and M. Ghiron (1983) Shape representation by rectangles preserving theirfractality, Proceedings, Sixth International Symposium on AutomatedCartography (AUTO-CARTO 6), 2, Oct. 16-21, Ottawa, 299-308.

Dutton, G. H. (1980) A fractal approach to the control of cartographic detail, Proceedings,Computer Graphics'80, Brighton, U.K., 371-381.

- 14 -

Dutton, G.H. (1981) Fractal enhancement of cartographic line detail, The AmericanCartographer, 8(1), 23-40.

Hill Jr., F. S., and S. E. Walker Jr. (1982) On the use of fractals for efficient map generation,Proceedings, Graphics Interface'82, May 17-21, Toronto, 283-289.

Janinski, M. J. (1990) The Comparison of Complexity Measures for CartographicLines. NCGIA Technical Report 90-1, Santa Barbara, California.

Maguire, D. J. (1986) Generalization, fractals and spatial databases, The Bulletin of theSociety of University Cartographers, 20(2), 96-99.

Muller, J.-C. (1986) Fractal dimension and inconsistencies in cartographic linerepresentations, The Cartographic Journal, 23(2), 123-130.

Muller, J.-C. (1987) Fractal and automated line generalization, The Cartographic Journal,24(1), 27-34.

Muller, J.-C. (1987) Optimal point density and compaction rates for the representation ofgeographic lines, Proceedings, Eighth International Symosium on Computer-Assisted Cartography (AUTO-CARTO 8), March 29-April 3, Baltimore,Maryland, 221-230.

III.2 LENGTH ESTIMATES AND SELF-SIMILIARITY OF LINES

Baugh, I. D., and J. R. Boreham (1976) Measuring the coastline from maps: A study of theScottish mainland, The Cartographic Journal, 13(2), 167-171.

Beckett, P. (1977) Cartographic generalizations, The Cartographic Journal, 14(1), 49-50.

Biddy, J. (1972) Infinite rivers and Steinhaus' paradox, Area, 4, 214.

Bruckstein, A. M. (1990) The self-similarity of digital straight lines, Proceedings, 10thInternational Conference on Pattern Recognition, 1, June 16-12, Atlantic City,New Jersey, IEEE Computer Society, 485-490.

Dorst, L., and A. W. M. Smeulders. (1987) Length estimation for digitized contours,Computer Vision, Graphics and Image Processing, 40(3), 311-333.

Ellis, T. J., and D. Proffitt (1979) Measurement of the lengths of digitized curved lines,Computer Graphics and Image Processing, 10(4), 333-347.

Galloway, R. W., and M. E. Bahr (1979) What is the length of the Australian coast?Australian Geographer, 14(4), 244-247.

Håkanson, L. (1978) The length of closed geomorphic lines, Mathematical Geology,10(2), 141-167.

- 15 -

Håkanson, L. (1981) The length of open geomorphic lines, Zeitschrift fürGeomorphologie, 25(4), 369-382.

Kappraff, J. (1986) The geometry of coastlines: a study in fractals, Computers andMathemathics with Applications, 12B(3/4), 655-671.

Ling, F. F. (1987) Scaling law for contoured length of engineering surfaces, Journal ofApplied Physics, 62(2), 2570-2572.

Longley, P. A., and M. Batty (1987) Using fractal geometry to measure maps and simulatecities, Computer Education, 56, 15-19.

Longley, P. A., and M. Batty (1988) Measuring and simulating the structure and form ofcartographic lines, in Developments in Quantitative Geography, J. Hauer, H.J.P.Timmermans and N. Wrigley, editors, Reidel Publishing, Dordecht.

Longley, P. A., and M. Batty (1989) On the fractal measurement of geographical boundaries,Geographical Analysis, 21(1), 47-67.

Luk'yanova, S. A., and N. A. Kholodilin (1975) Length of the shoreline of the world oceanand of various types of shores and coasts, Soviet Hydrology, 2, 66-69.

Maling, D. M. (1968) How long is a piece of string? The Cartographic Journal, 5(1),147-156.

Mandelbrot, B. B. (1967) How long is the coast of Britian? Statistical self-similarity andfractional dimension, Science, 156, 543-553.

Perkal, J. (1966) On the Length of Empirical Curves. Michigan Inter-UniversityCommunity of Mathematical Geographers, Discussion Paper No. 10, 34 pp. [translatedby R. Jackowski]

Richardson, L. F. (1961) The problem of contiguity: An appendix to 'Statistics of DeadlyQuarrels', in General Systems Yearbook, 6, 139-187.

Shelberg, M. C., H. Moellering, and N. Lam (1982) Measuring the fractal dimensions ofempirical cartographic curves, Proceedings, Fifth International Symposium onComputer-Assisted Cartography (AUTO-CARTO 5), August 22-28, CrystalCity, Virginia, 481-490.

Steinhaus, H. (1954) Length, shape and area, Colloquium Mathematicum, III(1), 1-13.

Underwood, J. D. M. (1981) Influencing the perception of contour lines, The CartographicJournal, 18(2), 116-119.

III.3 VISUAL PERCEPTION

Cutting, J. E., and J. J. Garvin (1987) Fractal curves and complexity, Perception &Psychophysics, 42(4), 365-370.

- 16 -

Knill, D. C., D. Field, and D. Kersten (1990) Human discrimination of fractal images,Journal of the Optical Society of America A, 7(6), 1113-1123.

Rensink, R. A. (1987) On the visual discrimination of self-similar random textures,Proceedings, Workshop on Computer Vision, Nov. 30-Dec. 2, Miami Beach,Florida, IEEE Computer Society, 240-242.

III.4 TERRAIN CHARACTERIZATION

Ahnert, F. (1984) Local relief and the height limits of mountain ranges, American Journalof Science, 284(9), 1035-1055.

Ansoult, M. M. (1989) Circular sampling for fourier analysis of digital terrain data,Mathematical Geology, 21(4), 401-410.

Barenblatt, G. I., A. V. Zhivago, Y. P. Neprochniv, and A. A. Ostrovskiy (1985) The fractaldimension: A quantitative characterization of ocean-bottom relief, Oceanology(USSR), 24(6), 695-697.

Berry, M. V., and J. H. Hannay (1978) Topography of random surfaces, Nature, 273, 573.

Clarke, K. C. (1986) Computation of the fractal dimension of topographic surfaces using thetriangular prism surface area method, Computers & Geosciences, 12(5), 713-722.

Clarke, K. C. (1987) Scale-based simulation of topography, Proceedings, EighthInternational Symosium on Computer-Assisted Cartography (AUTO-CARTO 8), March 29-April 3, Baltimore, Maryland, 680-688.

Clarke, K. C. (1988) Scale-based simulation of topographic relief, The AmericanCartographer, 15(2), 173-181.

Culling, W. E. H., and M. Datko (1987) The fractal geometry of the soil-covered landscape,Earth Surface Processes and Landforms, 12(4), 369-385.

Edwards, G. J. (1984) Fractal based terrain modelling, Proceedings, Conference onComputer Animation and Digital Effects, October, London, 49-56.

Elliot, J. K. (1989) An investigation of the change in surface roughness through time on theforeland of Austre Okstindbreen, North Norway, Computers & Geosciences, 15(2),209-217.

Fellous, A., J. Granara, and J. Hourcade (1985) Fractional Brownian relief: an exact localmethod, in Proceedings of Eurographics '85, North Holland, New York, 353-363.

Finlay, W. M. (1987) Fractal terrain image synthesis for simulation using Defense MappingAgency data, Infrared Image Processing and Enhancement, Proceedings ofSPIE, 781, May 20-21, Orlando, Florida, 58-62.

- 17 -

Fournier, A., and D. Fussell (1980) Stochastic modelling in computer graphics, ComputerGraphics, 14(6), 1-14.

Fournier, A., D. Fussell, and L. Carpenter (1982) Computer rendering of stochastic models,Communications of the ACM, 25(6), 371-384.

Fournier, A., D. Fussell, and L. Carpenter (1982) Author's rely to comments on computerrendering of fractal stochastic models by B. B. Mandelbrot, Communications of theACM, 25(8), 583-584.

Fox, C. G. (1987) An inverse fourier transform algorithm for generating random signals of aspecified spectral form, Computers and Geoscience,13(3), 1-6.

Fox, C. G. (1989) Empirically derived relationships between fractal dimension and power lawform frequency spectra, Pure and Applied Geophysics, 131(1/2), 211-239.

Fox, C. G., and D. E. Hayes (1985) Quantitative methods for analyzing the roughness of thesea-floor, Reviews of Geophysics and Space Physics, 23(1), 1-48.

Frederiksen, P., O. Jacobi, and K. Kubik (1985) A review of current trends in terrainmodelling, ITC Journal, 2, 101-106.

Gagalowicz, A., and S. De Ma Inria (1986) Model driven synthesis of natural textures for 3-Dscenes, Computing and Graphics, 10(2), 161-170.

Gilbert, L. E. (1988) A characterization of the spectral density of residual ocean floortopography, Geophysical Research Letters, 15(12), 1401-1404.

Gilbert, L. E. (1989) Are topographic data sets fractal?, Pure and Applied Geophysics,131(1/2), 241-254.

Goff, J. A. (1990) Fractal mapping of digitized images - application to the topography ofArizona and comparisons with synthetic-images - comment, Journal of GeophysicalResearch, 95(NB4), 5159.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: Inversionof sea beam data for second-order statistics, Journal of Geophysical Research, 93,13589-13609.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: Aparameterized Gaussian model, Geophysical Research Letters, 16(1), 45-48.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: Resolutionof topographic parameters by sea beam data, IEEE Journal of OceanicEngineering, 14(4), 326-337.

Goodchild, M. F. (1982) The Fractional Brownian process as a terrain simulation model,Modeling and Simulation, 13(3), Proceedings of the Thirteenth Annual PittsburghConference, 1133-1137.

- 18 -

Goodchild, M. F. (1988) Lakes on fractal surfaces: A null hypothesis for lake-rich landscapes,Mathematical Geology, 20(6), 615-630.

Harger, R. O. (1990) SAR object detection with fractal terrain models, Proceedings,International Geoscience and Remote Sensing Symposium (IGARSS'90), I,May 20-24, College Park, Maryland, 313-316.

Herbert, F. (1984) Fractal landscape modelling using octrees, IEEE Computer Graphicsand Applications, 4, 4-5.

Huang, J., and D. L. Turcotte (1989) Fractal mapping of digitized images - application to thetopography of Arizona and comparisons with synthetic-images, Journal ofGeophysical Research, 94(NB6), 7491-7495.

Huang, J., and D. L. Turcotte (1990) Fractal mapping of digitized images - application to thetopography of Arizona and comparisons with synthetic-images - reply to comment,Journal of Geophysical Research, 95(NB9), 5161.

Huang, J., and D. L. Turcotte (1990) Fractal image-analysis - application to the topography ofOregon and synthetic-images, Journal of the Optical Society of America A -Optics and Image Science, 7(6), 1124-1130.

Jeffrey, T. (1987) Mimicking mountains, BYTE, 12(12), 337-338,340,342,344.

Klinkenberg, B. (1988) Tests of a Fractal Model of Topography. Unpublished PhDdissertation, Department of Geography, University of Western Ontario, London, Ontario.

Kubik, K., and F. Leberl (1986) Fractal behavior of terrain topography, Technical Papersof the 52nd Annual Meeting of the American Society of Photogrammetryand Remote Sensing, 4, Washington, D.C., 186-190.

Laverty, M. (1987) Fractals in karst, Earth Surface Processes and Landforms, 12,475-48O.

Malinverno, A. (1989) Segmentation of topographic profiles of the seafloor based on a self-affine model, IEEE Journal of Oceanic Engineering, 14(4), 348-359.

Malinverno, A. (1989) Testing linear models of sea-floor topography, Pure and AppliedGeophysics, 31(1/2), 139-155.

Mandelbrot, B. B. (1982) Comment on computer rendering of fractal stochastic models,Communications of the ACM, 25(8), 581-584.

Mandelbrot, B. B. (1988) Fractal landscapes without creases and with rivers, in TheScience of Fractal Images, H.-O. Peitgen and D. Saupe, editors, Springer-Verlag,New York, 243-260.

Mareschal, J.-C. (1989) Fractal reconstruction of sea-floor topography, Pure and AppliedGeophysics, 131(1/2), 197-210.

- 19 -

Mark, D. M., and P. B. Aronson (1984) Scale-dependent fractal dimensions of topographicsurfaces: An empirical investigation with application in geomorphology and computermapping, Mathematical Geology, 16(7), 671-683.

Miller, G. S. P. (1986) The definition and rendering of terrain maps, Computer Graphics,20(4), 39-48.

Muller, J.-P., and T. Saksono (1986) An evaluation of the potential role of fractals for digitalelevation model generation from spaceborne imagery, Proceedings, InternationalSymposium of the ISPRS Commission IV and Remote Sensing Society,Sept. 8-12, Edinburgh, Scotland, 63.

Norton, D., and S. Sorenson (1989) Variations in geometric measures of topographic surfacesunderlain by fractured granitic plutions, Pure and Applied Geophysics, 131(1/2),77-97.

Pentland, A. P. (1987) Fractal surface models for communication about terrain, VisualCommunications and Image Processing II, Proceedings of SPIE, 845, 301-307.

Piech, M. A., and K. R. Piech (1990) Fingerprints and fractal terrain, MathematicalGeology, 22(4), 457-485.

Rees, D., and J. P. Muller (1990) Surface roughness estimation using fractal variogramanalysis, Proceedings, International Geoscience and Remote SensingSymposium (IGARSS'90), III, May 20-24, College Park, Maryland, 1951-1954.

Roy, A. G., G. Gravel, and C. Guathier (1987) Measuring the dimension of surfaces: Areview and appraisal of different methods, Proceedings, Eighth InternationalSymosium on Computer-Assisted Cartography (AUTO-CARTO 8), March29-April 3, Baltimore, Maryland, 68-77.

Sayles, R. S., and T. R. Thomas (1978) Surface topography as a nonstationary randomprocess, Nature, 271, 431-434.

Smith, D. K., and P. R. Shaw (1989) Using topographic slope distributions to infer seafloorpatterns, IEEE Journal of Oceanic Engineering, 14(4), 338-347.

Steyn, D. B., and K. W. Ayotte (1985) Application of two-dimension terrain height spectra tomesoscale modeling, Journal of Atmospheric Sciences, 42, 2884-2887.

Turcotte, D. L. (1987) A fractal interpretation of topography and geoid spectra on the Earth,Moon, Venus and Mars, Journal of Geophysical Research, 92(B4), E597-E601.

Willers, C. J. (1988) Applications of fractal geometry to modelling nature, Proceedings,South African Conference on Communications and Signal Processing(COMSIG 88), June 24, Pretoria, IEEE, 123-129.

Yokoya, N., and K. Yamamoto (1989) Fractal-based analysis and interpretation of 3D naturalsurface shapes and their application to terrain modeling, Computer Vision, Graphics,and Image Processing, 46(3), 284-302.

- 20 -

III.5 METEOROLOGY

Baryshnikova, Y. S., G. M. Zaslavsky, E. A. Lupyan, S. S. Moiseyev, and F. Pinter (1989)Fractal analysis of the pre-hurricane atmosphere from satellite data, in Remote Sensingof Atmosphere and Ocean, Advances in Space Research, 9, Pergamon Press,Oxford, 393-404.

Beer, T. (1989) Modeling rainfall as a fractal process, Mathematics and Computers inSimulation, 32(1/2), 119-124.

Cahalan, R. F. (1987) Overview of fractal clouds, in Advances in Remote SensingRetrieval Methods, A. Deepak, H.E. Fleming and J.S. Theon, editors, A. DeepakPublishing, Hampton, Virginia, 371-389.

Cahalan, R. F., and J. H. Joseph (1989) Fractal statistics of cloud fields, Monthly WeatherReview, 117(2), 261-272.

Carter, P. H. et al. (1986) Dimension measurements from cloud radiance, in Dimensionsand Entropies in Chaotic Systems, G. Mayer-Kress, editor, Springer-Verlag,Berlin, 215-221.

Davis, A., P. Gabriel, S. Lovejoy, D. Schertzer, and G. L. Austin (1990) Discrete angleradiative-transfer. 3. Numerical results and meteorological applications, Journal ofGeophysical Research A, 95(D8), 1729-1742.

Fraedrich, K., R. Grotjahn, and L. M. Leslie (1990) Estimates of cylone track predictability.2. Fractal analysis of midlatitude cyclones, Quarterly Journal of the RoyalMeteorlogical Society, 116(492), 317-335.

Gabriel, P., S. Lovejoy, and D. Schertzer (1988) Resolution dependence in satellite imagery -multifractal analysis, Third Conference on Satellite Meteorology andOceanography (Preprint), Feb. 1-5, Anaheim, California, 392-394.

Gabriel, P., S. Lovejoy, A. Davis, D. Schertzer, and G. L. Austin (1990) Discrete angleradiative-transfer. 2. Renormalization approach for homogeneous and fractal clouds,Journal of Geophysical Research A, 95(D8), 1717-1728.

Gupta, V. K., and E. Waymire (1990) Multiscaling properties of spatial rainfall and river flowdistributions, Journal of Geophysical Research, 95(D3), 1999-2010.

Henderson-Sellers, A. (1986) Are Martian clouds fractal?, Royal Astronomical Society,Quarterly Journal, 27, 90-93.

Hentschel, H. G. E., and I. Procaccia (1984) Relative diffusion in turbulent media - the fractaldimension of clouds, Physical Review A, 29, 1461-1470.

Kai, S., S. Ikuta, S. C. Muller, and T. Yamada (1989) Fractal geometry of precipitationpatterns, Journal of the Physical Society of Japan, 58(10), 3445-3448.

- 21 -

Kedem, B., and L. S. Chiu (1987) Are rain rate processes self-similar? Water ResourcesResearch, 23, 1816-1818.

Lovejoy, S. (1982) Area-perimeter relation for rain and cloud areas, Science, 216(9), 185-187.

Lovejoy, S. (1983) La géométrie fractale des nauges et des regions de pluie et les simulationsaléatoires, Houile Blanche, 516, 431-436.

Lovejoy, S., A. Davis, P. Gabriel, D. Schertzer and G. L. Austin (1990) Discrete angleradiative-transfer. 1. Scaling and discrete similarity, universality and diffusion, Journalof Geophysical Research A, 95(D8), 1699-1715.

Lovejoy, S., P. Gabriel, G. L. Austin, D. Schertzer (1988) Modeling the scale dependence ofvisible satellite images by radiative-transfer in fractal clouds, Third Conference onSatellite Meteorology and Oceanography (Preprint) , Feb. 1-5, Anaheim,California, 395-400.

Lovejoy, S., and B. B. Mandelbrot (1985) Fractal properties of rain, and a fractal model,Tellus, 37A(3), 209-232.

Lovejoy, S., and D. Schertzer (1985) Generalized scale invariance in the atmosphere andfractal models of rain, Water Resources Research, 21(8), 1233-1250.

Lovejoy, S., and D. Schertzer (1985) Rainfronts, fractals and rainfall simulation, inHydrological Applications of Remote Sensing and Remote DataTransmission, B.E. Goodison, editor, International Association of HydrologicalSciences (IAHS) publication no. 145, Wallingford, Oxfordshire, U.K., 323-334.

Lovejoy, S., and D. Schertzer (1986) Scale invariance, symmetries, fractals, and stochasticsimulations of atmospheric phenomena, Bulletin of the American MeteorologicalSociety, 67(1), 21-32.

Lovejoy, S., and D. Schertzer (1986) Scale invariance in climatological temperatures and thelocal spectra plateau, Annales Geophysicae, 4(B4), 401-410.

Lovejoy, S., and D. Schertzer (1988) Meeting reports: Scaling, fractals, and nonlinearvariability in geophysics, Eos, 69(10), 143-145.

Lovejoy, S., and D. Schertzer (1989) Comment on 'Are rain rate processes self-similar?' byB. Kedem and L.S. Chiu, Water Resources Research, 25(3), 577-579.

Lovejoy, S., and D. Schertzer (1990) Multifractals, universality classes and satellite and radarmeasurements of cloud and rain fields, Journal of Geophysical Research, 95(D3),2021-2034.

Lovejoy, S., D. Schertzer, and P. Ladoy (1986) Fractal characterization of inhomogeneousgeophysical measuring networks, Nature, 319, 43-44.

Lovejoy, S., D. Schertzer, and A. A. Tsonis (1987) Functional box-counting and multipleellipitical dimensions in rain, Science, 235, 1036-1038.

- 22 -

Nelson, J. (1989) Fractality of sooty smoke - implications for the severity of nuclear winter,Nature, 339, 611-613.

Rys, F. S., and A. Waldvogel (1986) Analysis of the fractal shape of severe convectiveclouds, in Fractals in Physics, L. Pietronero and E. Tosatti, editors, North-Holland,New York, 461-464.

Rys, F. S., and A. Waldvogel (1986) Fractal shape of hail clouds, Physical ReviewLetters, 56(7), 784-787.

Schertzer, D., and S. Lovejoy (1984) On the dimension of atmospheric motion, inTurbulence and Chaotic Phenomena in Fluids, T. Tatsumi, editor, Elsevier, NewYork, 43-61.

Schertzer, D., and S. Lovejoy (1985) Generalized scale invariance in turbulent phenomena,PhysicoChemical Hydrodynamics, 6(5/6), 623-635.

Schertzer, D., and S. Lovejoy (1987) Physically based rain and cloud modeling byanisotropic, multiplicative turbulent cascades, Journal of Geophysical Research,92, 9693-9714.

Schertzer, D., and S. Lovejoy (1989) Nonlinear variability in geophysics - multifractalsimulations and analysis, in Fractals: Physical Origin and Properties, L.Pietronero, editor, Plenum, New York, 49-82.

Selvan, M. A. (1989) Deterministic chaos model for self-organized adaptive networks inatmospheric flows, Proceedings, IEEE National Aerospace and ElectronicsConference (NAECON), 3, May 22-26, Dayton, Ohio, 1145-1152.

Skoda, G. (1987) Fractal dimension of rainbands over hilly terrain, Meteorology andAtmospheric Physics, 36, 74-82.

Steyn, D. B., and K. W. Ayotte (1985) Application of two-dimension terrain height spectra tomesoscale modeling, Journal of Atmospheric Sciences, 42, 2884-2887.

Tabler, R. D. (1980) Self-similarity of wind profiles in blowing snow allows outdoormodeling, Journal of Glaciology, 26, 421-434.

Waymire, E. (1985) Scaling limits and self-similarity in precipitation fields, WaterResources Research, 21(8), 1251-1265.

Zawadzki, I. (1987) Fractal structure and exponential decorrelation in rain, Journal ofGeophysical Research - Atmospheres, 92(ND8), 9586-9690.

III.6 OCEANOGRAPHY

Barenblatt, G. I., A. V. Zhivago, Y. P. Neprochniv, and A. A. Ostrovskiy (1985) The fractaldimension: A quantitative characterization of ocean-bottom relief, Oceanology (USSR),24(6), 695-697.

- 23 -

Baryshnikova, Y. S., G. M. Zaslavsky, E. A. Lupyan, S. S. Moiseyev, and E. A. Sharkov(1989) Fractal analysis of the pre-hurricane atmosphere from satellite data, in RemoteSensing of Atmosphere and Oceans, Advances in Space Research, 9,Pergamon Press, Oxford, 405-408.

Bishop, G. C., and S. E. Chellis (1989) Fractal dimension - A descriptor of ice keel surface-roughness, Geophysical Research Letters, 16(9), 1007-1010.

Fox, C. G., and D. E. Hayes (1985) Quantitative methods for analyzing the roughness of thesea-floor, Reviews of Geophysics and Space Physics, 23(1), 1-48.

Gilbert, L. E. (1988) A Characterization of the spectral density of residual ocean floortopography, Geophysical Research Letters, 15(12), 1401-1404.

Glazman, R. E. (1988) Fractal features of sea-surface manifested in microwave remote-sensingsignatures, Wave Propagation and Scattering in Varied Media, Proceedings ofSPIE, 927, 150-153.

Glazman, R. E. (1988) Fractal properties of the sea-surface manifested in microwave remotesensing signatures, Proceedings, International Geoscience and RemoteSensing Symposium (IGARSS'88), 3, Sept. 13-16, Edinburgh, Scotland,European Space Agency SP-284, 1623-1624.

Glazman, R. E., and N. N. Filonenki (1989) Statistical geometry of a small patch in adeveloped sea, Journal of Geophysical Research, 94, 4998-5010.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: Inversionof sea beam Data for second-order statistics, Journal of Geophysical Research, 93,13589-13609.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: Aparameterized Gaussian model, Geophysical Research Letters, 16(1), 45-48.

Goff, J. A., and T. H. Jordan (1989) Stochastic modeling of seafloor morphology: resolutionof topographic parameters by sea beam data, IEEE Journal of OceanicEngineering, 14(4), 326-337.

Malinverno, A. (1989) Segmentation of topographic profiles of the seafloor based on a self-affine model, IEEE Journal of Oceanic Engineering, 14(4), 348-359.

Malinverno, A. (1989) Testing linear models of sea-floor topography, Pure and AppliedGeophysics, 131(1/2), 139-155.

Mareschal, J.-C. (1989) Fractal reconstruction of sea-floor topography, Pure and AppliedGeophysics, 131(1/2), 197-210.

Osborne, A.R. (1989) Fractal drifter trajectories in the Kuroshio Extension, Tellus, A41(5),416-435.

Rothrock, D. A., and A. S. Thorndike (1980) The geometric properties of the underside ofsea-ice, Journal of Geophysical Research, 85, 3955-3963.

- 24 -

Rothrock, D. A., and A. S. Thorndike (1984) Measuring the sea ice floe size distribution,Journal of Geophysical Research, 89(C4), 6477-6486.

Smith, D. K., and P. R. Shaw (1989) Using topographic slope distributions to infer seafloorpatterns, IEEE Journal of Oceanic Engineering, 14(4), 338-347.

III.7 GEOMORPHOLOGY/HYDROLOGY

Andrews, D. J. (1980) A stochastic fault model, Journal of Geophysical Research,85(B7), 3867-3877.

Andrle, R., and A. D. Abrahams (1989) Fractal techniques and the surface roughness of talusslopes, Earth Surface Processes and Landforms, 14(3), 197-209.

Andrle, R., and A. D. Abrahams (1990) Fractal techniques and the surface roughness of talusslopes - reply, Earth Surface Processes and Landforms, 15(3), 287-290.

Armstrong, A. C. (1986) On the fractal dimensions of some transient soil properties, Journalof Soil Science, 37(4), 641-651.

Aviles, C. A., C. H. Scholz, and J. Boatwright (1987) Fractal analysis applied tocharacteristic segments of the San Andreas Fault, Journal of Geophysical Research,92, 331-344.

Brown, S. R., and C. H. Scholz (1985) Broad bandwidth study of the topography of naturalrock surfaces, Journal of Geophysical Research, 90(B14), 12, 575-82.

Burrough, P. A. (1981) Fractal dimensions of landscapes and other environmental data,Nature, 294(19), 240-242.

Burrough, P. A. (1983) Multi-scale sources of spatial variation in soil: I. The application offractal concepts to nested levels of soil variation, Journal of Soil Science, 34(3), 577-598.

Burrough, P. A. (1983) Multi-scale sources of spatial variation in soil: II. A non-Brownianfractal model and its application to soil survey, Journal of Soil Science, 34(3), 599-620.

Burrough, P. A. (1983) Problems of superimposed effects in the statistical study of the spatialvariation of soil, Agricultural Water Management, 6(2), 123-144.

Burrough, P. A. (1984) The application of fractal ideas to geophysical phenomena, Instituteof Mathematics and its Applications, 20(3/4), 36-42.

Burrough, P. A. (1985) Fakes, facsimiles and facts: Fractal models of geophysicalphenomena, in Science and Uncertainty, S. Nash, editor, Science Reviews Ltd.,Middlesex, England, 151-169.

- 25 -

Burrough, P. A. (1987) Multiple sources of spatial variation and how to deal with them,Proceedings, Eighth International Symosium on Computer-AssistedCartography (AUTO-CARTO 8), March 29-April 3, Baltimore, Maryland, 145-154.

Church, M., and D. M. Mark (1980) On size and scale in geomorphology, Progress inPhysical Geography, 4(3), 343-390.

Culling, W. E. H. (1986) Highly erratic spatial variability of soil pH on Iping Common, WestSussex, Catena, 13(1), 81-89.

Culling, W. E. H. (1986) Hurst phenomena in the landscape, Transactions, JapaneseGeomorphological Union, 7(4), 1-25.

Culling, W. E. H. (1988) Dimension and entropy in the soil-covered landscape, EarthSurface Processes and Landforms, 13(7), 619-648.

Culling, W. E. H. (1989) The Characterization of regular/irregular surfaces in the soil-coveredlandscape by Gaussian eandom fields, Computers & Geosciences, 15(2), 219-226.

Culling, W. E. H., and M. Datko (1987) The fractal geometry of the soil-covered landscape,Earth Surface Processes and Landforms, 12(4), 369-385.

Curl, R. L. (1986) Fractal dimensions and geometries of caves, Mathematical Geometry,18(8), 765-783.

Goodchild, M. F., B. Klinkenberg, M. Glieca, and M. Hasan (1985) Statistics of hydrologicnetworks on fractional Brownian surfaces, Proceedings of the 16th AnnualPittsburgh Conference on Modeling and Simulation, University of Pittsburgh,16, 317-323.

Gupta, V. K., and E. Waymire (1990) Statistical self-similarity in river networksparameterized by elevation, Water Resources Research, 25(3), 463-476.

Hipel, K. W., and A. I. McLeod (1978) Preservation of the rescaled adjusted range. 3.Fractional gaussian noise algorithms, Water Resources Research, 14, 517-518.

Hjelmfelt, A. T. (1988) Fractals and the river length catchment area ratio, Water ResourcesBulletin, 24(2), 455-459.

Jones, J. G., R. W. Thomas, and P. G. Earwicker (1989) Fractal properties of computer-generated and natural geophysical data, Computers and Geosciences, 15(2), 227-235.

Kadanoff, L.P. (1989) Fractals and multifractals in avalanche models, Physica D, 38(1/3),213-214.

Kapoor, V. (1990) Spatial uniformity of power and the altitudinal geometry of river networks,Water Resources Research, 26(10), 2303-2310.

Kirkby, M. J. (1987) The Hurst effect and its implications for extrapolating process rates,Earth Surface Proceses and Landforms, 12(1), 57-67.

- 26 -

Klemes, V. (1974) The Hurst phenomenon: A puzzle?, Water Resources Research,10(4), 675-688.

La Barbera, P., and R. Rosso (1989) On the fractal dimension of stream networks, WaterResources Research, 25(4), 735-741.

La Barbera P., and R. Rosso (1990) Comment on 'On the fractal dimension of streamnetworks' by Paolo La Barbera and Renzo Rosso: Rely, Water Resources Research,26(9), 2245-2248.

Luk'yanova, S. A., and N. A. Kholodilin (1975) Length of the shoreline of the world oceanand of various types of shores and coasts, Soviet Hydrology, 2, 66-69.

Mandelbrot, B. B. (1967) How long is the coast of Britain? Statistical self-similarity andfractional dimension, Science, 156, 636-638.

Mandelbrot, B. B. (1969) Computer experiments with fractional gaussian noise generator,Water Resources Research, 5, 1-228.

Mandelbrot, B. B. (1971) A fast fractional gaussian noise generator, Water ResourcesResearch, 7, 543-553.

Mandelbrot, B. B. (1975) Stochastic models for the Earth's relief, the shape and the fractaldimension of coastlines, and the number-area rule for islands, Proceedings of theNational Academy of Sciences USA, 72, 3825-3828.

Mandelbrot, B. B., and J. R. Wallis (1968) Noah, Joseph, and operational hydrology, WaterResource Research, 4(5), 909-918.

Mandelbrot , B. B., and J. R. Wallis (1969) Computer experiments with fractional Gaussiannoises: Part 1, averages and variances, Water Resources Research, 5(1), 228-267.

Mandelbrot, B. B., and J. R. Wallis (1969) Robustness of the rescaled range R/S in themeasurement of noncyclic long-run statistical dependence, Water ResourcesResearch, 5, 967-988.

Mandelbrot, B. B., and J. R. Wallis (1969) Some long-run properties of geophysical records,Water Resources Research, 5(2), 321-340.

Mark, D. M., and P. B. Aronson (1984) Scale-dependent fractal dimensions of topographicsurfaces: an empirical investigation, with applications in geomorphology and computermapping, Mathematical Geology, 16(7), 671-683.

Mesa, O. J., and V. K. Gupta (1987) On the main channel length-area relationship for channelnetworks, Water Resources Research, 23(11), 2119-2122.

Okubo, P. G., and K. Aki (1987) Fractal geometry in the San Andreas Fault system, Journalof Geophysical Research, 92(1), 345-355.

Pape, H., and J. R. Schopper (1987) Stereological determination of grain-size distributions inconsolidated aggregates on the base of a fractal concept, Acta Stereologica, 6,supplement 3, parts 1-2, 827-832.

- 27 -

Phillips, J. D. (1986) Spatial analysis of shoreline erosion, Delaware Bay, New Jersey,Annals of the Association of American Geographers, 76(1), 50-62.

Robert, A. (1988) Statistical properties of sediment bed profiles in alluvial channels,Mathematical Geology, 20(3), 205-225.

Robert, A., and A. G. Roy (1990) On the fractal interpretation of the mainstream length-drainage area relationship, Water Resources Research, 26(5), 839-842.

Rodriguez-Iturbe, I., J. M. Mejia, and D. R. Dawdy (1972) Streamflow simulation; 1. A newlook at Markovian models, fractional Gaussian noise and crossing theory; 2. the brokenline process as a potential model for hydrological simulation, Water ResourcesResearch, 8(4), 921-941.

Roy, A. G., and A. Robert (1990) Fractal techniques and the surface roughness of talusslopes: A comment, Earth Surface Processes and Landforms, 15(3), 283-285.

Seiler, F. A. (1986) Use of fractals to estimate environmental diluation factors in river basins,Risk Analysis, 6, 15-25.

Snow, R. S. (1989) Fractal sinuosity of stream channels, Pure and Applied Geophysics,131(1/2), 99-109.

Tarboton, D. G. (1989) The Analysis of River Basins and Channel NetworksUsing Digital Terrain Data. Unpublished PhD dissertation, Department of CivilEngineering, MIT, Cambridge, Massachusetts.

Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1988) The fractal nature of rivernetworks, Water Resources Research, 24(8), 1317-1322.

Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1989) Scaling and elevation in rivernetworks, Water Resources Research, 25(9), 2037-2051.

Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1990) Comment on "On the fractaldimension of stream networks" by P. La Barbera and R. Rosso, Water ResourcesResearch, 26(9), 2243-2244.

Taylor, C. C., and P. A. Burrough (1986) Multiscale sources of variation in soil: III.improved methods for fitting the nested model to one-dimensional semivariograms,Mathematical Geology, 18(8), 811-821.

Tokunaga, E. (1984) Ordering of divide segments and law of divide segment numbers,Transactions, Japanese Geomorphological Union, 5, 71-77.

Van Pelt, J., M. J. Woldenberg, and R. W. H. Verwer (1989) Two generalized topologicalmodels of stream network growth, Journal of Geology, 97, 281-199.

- 28 -

III.8 HYDRAULICS AND FLUID MECHANICS

Frisch, U. (1985) Fully developed turbulence and intermittency, in Turbulence andPredictability in Geophysical Fluid Dynamics and Climate Dynamics, M.Ghil, R. Benzi and G. Parisi, editors, North-Holland, New York, 71-88.

Mandelbrot, B. B. (1974) Intermittent turbulence in self-similar cascades, divergence of highmoments and dimension of the carrier, Journal of Fluid Mechanics, 62(2), 331-358.

Meneveau, C. (1989) The multifractal Nature of Turbulence. PhD dissertation,Department of Physics, Yale University, New Haven, Connecticut.

Orszag, S. A. (1984) Instabilities and turbulence, in Turbulence and ChaoticPhenomena in Fluids, T. Tatsumi, editor, Elsevier, New York, 73-83.

Prassad, R. R., and K. R. Sreenivasan (1990) The measurement and interpretation of fractaldimensions of the scalar interface in turbulent flows, Physics of Fluids A - FluidDynamics, 2(5), 792-807.

Schneider, S. P. (1990) Free-stream turbulence - a limitation on fractal descriptions of open-flow systems, Physics of Fluids A - Fluid Dynamics, 2(5), 869-872.

Sreenivasan, K. R., and C. Meneveau (1986) The Fractal facets of turbulance, Journal ofFluid Mechanics, 173, 357-386.

Sreenivasan, K. R., R. R. Prasad, C. Meneveav, and R. Ramshankar (1989) The fractalgeometry of interfaces and the multifractal distribution of dissipation in fully turbulentflows, Pure and Applied Geophysics, 131(1/2), 43-60.

Sreenivasan, K. R., R. Ramshandar, and C. Meneveau (1989) Mixing, entrainment andfractal dimensions of surfaces in turbulent flows, Proceedings of the Royal SocietyA, 421(1860), 79-107.

Sreenivasan, K. R., and P.J. Strykowski (1984) On analogies between turbulence in openflows and chaotic dynamical systems, in Turbulence and Chaotic Phenomena inFluids, T. Tatsumi editor, Elsevier, New York, 191-196.

Turcotte, P. L. (1988) Fractals in fluid mechanics, Annual Review of Fluid Mechanics,20, 5-16.

III.9 EARTH SCIENCES

Allegre, C. J., J. L. LeMouel, and A. Provost (1982) Scaling rules in rock fracture andpossible implications for earthquake prediction, Science, 297, 47-49.

Armstrong, A. C. (1986) On the fractal dimensions of some transient soil properties, Journalof Soil Science, 37, 641-652.

- 29 -

Aviles, C. A., and C. H. Scholz (1985) Fractal analysis of characteristic fault segments of theSan Andres fault system, Eos, 66, 314-321.

Aviles, C. A., C. H. Scholz, and J. Boatwright (1987) Fractal analysis applied tocharacteristic segments of the San Andreas fault, Journal of Geophysical Research,92(B1), 331-344.

Bak, P.m and C. Tang (1989) Earthquakes as a self-organized critical phenomena, Journalof Geophysical Research, 94(B11), 15635-15637.

Barton, C., and E. Larson (1985) Fractal geometry of two-dimensional fracture networks atYucca Mountain, south-west Nevada, in Fundamentals of Rock Joints,Proceedings of the International Symposium on Fundamentals of RockJoints, Bjorklinden, Sweden, 77-84.

Benohoud, M., and H. Vandamme (1990) The fractal texture of swelling clays and clay-organic aggregates, Comptes Rendus de L'Academie des Sciences, Serie II,311(6), 665-670.

Biegel, R. L., C. G. Sammis, and J. H. Dieterich (1989) The frictional-properties of asimulated gouge having a fractal particle distribution, Journal of Structural Geology,11(7), 827.

Brown, S. R. (1987) A note on the description of surface-roughness using fractal dimension,Geophysical Research Letters, 14(11), 1095-1098.

Brown, S. R., and C. H. Scholz (1985) Broad bandwidth study of the topography of naturalrock surfaces, Journal of Geophysical Research, 90(B14), 12575-12582.

Burrough, P. A. (1981) Fractal dimensions of landscapes and other environmental data,Nature, 294, 240-242.

Burrough, P. A. (1983) Multiscale sources of spatial variation in soil. 1. The application offractal concepts to nested levels of soil variation, Journal of Soil Science, 34, 577-597.

Burrough, P. A. (1983) Multiscale sources of spatial variation in soil. 2. A non-Brownianfractal model and its application in soil survey, Journal of Soil Science, 34, 599-620.

Burrough, P. A. (1988) Fractals and geochemistry, in The Fractal Approach to theChemistry of Disordered Systems, D. Avnir, editor, John Wiley & Sons, NewYork.

Chelidze, T., and V. Gueguen (1990) Evidence of fractal fracture, International Journalof Rock Mechanics and Mining Science & Geomechanics Abstracts, 27(3),223-225.

Chiles, J. P. (1988) Fractal and geostatistical methods for modeling of a fracture network,Mathematical Geology, 20(6), 631-654.

Crossley, D. J., and O. G. Jensen (1989) Fractal velocity models in refraction seismology,Pure and Applied Geophysics, 131(1/2), 61-76.

- 30 -

Davis, H. T. (1989) On the fractal character of the porosity of natural sandstone,Europhysics Letters, 8(7), 629-632.

Davy, P., A. Sornette, and D. Sornetto (1990) Some consequences of a proposed fractalnature of continental faulting, Nature, 348(6296), 56-58.

Dearnley, R. (1985) Effects of resolution on the measurement of grain 'size', MineralogicalMagazine, 49(4), 539-546.

Dubois, J., and L. Nouaili (1989) Quantification of the fraturing of the slab using a fractalapproach, Earth and Planetary Science Letters, 94(1/2), 97-108.

Dziewonski, A. M., and A. G. Prozorov (1984) Self-similar determination of earthquakeclustering, Computational Seismology, 16, 7-16.

Fluegeman Jr., R. H., and R. S. Snow (1989) Fractal analysis of long-range paleoclimaticdata: Oxygen isotope record of Pacific core V28-29, Pure and Applied Geophysics,131(1/2), 307-313.

Frisch, A. A., D. A. Evans, J. P. Hudson, and J. Boon (1987) Shape discrimination of sandsamples using the fractal dimension, in Coastal Sediments'87, N.C. Kraus, editor,138-153.

Hansen, J. P., and A. T. Skjeltorp (1988) Fractal pore-space and rock permeabilityimplications, Physical Review B, 38(4), 2635-2638.

Hayward, J., J. D Orford, and W. B. Whalley (1989) Three implementations of fractal analysisof particle outlines, Computers & Geosciences, 15(2), 199-208.

Hirata, T. (1989) A correlation between the B-value and the fractal dimension of earthquakes,Journal of Geophysical Research, 94(NB6), 7506-7514.

Hirata, T. (1989) Fractal dimension of fault systems in Japan: Fractal structure in rock fracturegeometry at various scales, Pure and Applied Geophysics, 131(1/2), 157-170.

Jacquin, C. G., and P. M. Alder (1987) Fractal geological structures, Acta Stereologica, 6,supplement 3, parts 1-2, 821-826.

Kagan, Y. Y., and L. Knopoff (1981) Stochastic synthesis of earthquake catalogs, Journalof Geophysical Research B, 86(4), 2853-2862.

Katz, A.J., and A.H. Thompson (1985) Fractal sandstone pores: Implications for conductivityand pore formation, Physical Review Letters, 54, 1325-1328.

King, G. (1983) The accomodation of large strains in the upper lithosphere of the Earth andother solids by self-similar fault systems: the geometrical origin of b-value, Pure andApplied Geophysics, 121, 761-815.

Korvin, G. (1989) Fractured but not fractal: Fragmentation of the Gulf of Suez basement,Pure and Applied Geophysics, 131(1/2), 289-305.

- 31 -

Krohn, C. E. (1988) Fractal measurements of sandstones, shales, and carbonates, Journalof Geophysical Research, 93(B4), 3297-3305.

Krohn, C. E. (1988) Sandstone fractal and Euclidean pore volume distributions, Journal ofGeophysical Research, 93(B4), 3286-3296.

Krohn, C. E., and A. H. Thompson (1986) Fractal sandstone pores: Automated measuringusing scanning-electron microscope images, Physical Review B, 33, 6366-6374.

Kumar, S., and G. S. Bodvarsson (1990) Fractal study and simulation of fracture roughness,Geophysical Research Letters, 17(6), 701-704.

Lang, B., and K. Franaszczuk (1986) Fractal viewpoint of fragmentation of the Lowiczmeteorite, Meteorites, 21(4), 428.

Lapointe, P. R. (1988) A method to characterize fracture density and connectivity throughfractal geometry, International Journal of Rock Mechanics and MiningScience & Geomechanics Abstracts, 25(6), 421-429.

Laverty, M. (1987) Fractals in karst, Earth Surface Processes and Landforms, 12(5),475-480.

Lenormand, R. (1989) Application of fractal concepts in petroleum engineering, Physica D,38(1/3), 230-234.

Leonard, J. E. (1988) Fractal geometry: From Star Trek to fractured reservoirs, Geobtye,3(1), 60.

Levi, B. G. (1990) Are fractures fractal or quakes chaotic? Physics Today, 43:11, 17-19.

Lovejoy, S., and D. Schertzer (1988) Scaling, fractals, and nonlinear variability ingeophysics, Eos, 69(10), 143-145.

Lovejoy, S., D. Schertzer, and P. Ladoy (1986) Fractal characterization of inhomogeneousgeophysical measuring networks, Nature, 319, 43-44.

Madden, T. R. (1983) Microcrack connectivity in rocks: A renormalization group approach tothe critical phenomena of conduction and failure in crystaline rocks, Journal ofGeophysical Research, 88, 585-592.

Mandelbrot, B. B. (1989) Multifractal measures, especially for the geophysicist, Pure andApplied Geophysics, 131(1/2), 5-42.

Matsuhita, M. (1985) Fractal viewpoint of fracture and accretion, Journal of the PhysicalSociety of Japan, 54(3), 857-860.

Mecholsky, J. J. (1986) Fractals - fact or fiction?, Earth and Mineral Sciences, 55(3),29-33.

Nolte, D. D., L. J. Pyrak-Nolte, and N. G. W. Cook (1989) The fractal geometry of flowpaths in natural fractures in rock and the approach to percolation, Pure and AppliedGeophysics, 131(1/2), 111-138.

- 32 -

Okubo, P. G., and K. Aki (1987) Fractal geometry in the San Andreas fault system, Journalof Geophysical Research, 92(B1), 345-355.

Orford, J. D., and W. B. Whalley (1983) The use of fractal dimension to quantify themorphology of irregular-shaped particles, Sedimentology, 30(5), 655-668.

Plotnick, R. E. (1986) A Fractal model for the distribution of stratigraphic hiatuses, Journalof Geology, 94(6), 885-890.

Plotnick, R. E. (1988) A Fractal model for the distribution of stratigraphic hiatuses: A reply,Journal of Geology, 96(1), 102-103.

Power, W. L., T. E. Tullis, S. R. Brown, G. N. Boitnott, and C. H. Scholz (1987)Roughness of natural fault surfaces, Geophysical Research Letters, 14(1), 29-32.

Roberts, J. N. (1986) Fractal sandstone pores - comment, Physical Review Letters,56(19), 2111.

Ross, B. (1986) Dispersion in fractal frature networks, Water Resources Research, 22,823-827.

Rydelek, P. A., and I. S. Sacks (1989) Testing the completeness of earthquake catalogues andthe hypothesis of self-similarity, Nature, 337, 251-253.

Sammis, C. G., and R. L. Biegel (1989) Fractals, fault-gouge, and friction, Pure andApplied Geophysics, 131(1/2), 255-271.

Sammis, C. G., R. H. Osborne, J. L. Anderson, M. Banerdt, and P. White (1986) Self-similar cataclais in the formation of fault gouge, Pure and Applied Geophysics, 123,53-78.

Scholz, C. H. (1982) Scaling laws for large earthquakes, Bulletin of the SeismologicalSociety of America, 72, 1-14.

Scholz, C. H., and C. A. Aviles (1986) The Fractal geometry of faults and faulting in 5thEwing Symposium, Earthquake Source Mechanisms, Geophysical MonographSeries 37, S. Das, J. Boatwright, and C. H. Scholz, editors, American GeophysicalUnion, Washington, D.C., 147-156.

Smalley Jr., R. F., J.-L. Chatelain, D. L. Turcotte, and R. Prévot (1987) A fractal approachto the clustering of earthquakes: applications to the seismicity of the New Herbrides,Bulletin of the Seismological Society of America, 7(4), 1368-1381.

Smalley Jr., R. F., D. L. Turcotte, and S. A. Solla (1985) A renormalization group approachto the stick behavior of faults, Journal of Geophysical Research, 90, 1894-1900.

Sornette, A., and D. Sornette (1989) Self-organized criticality and earthquakes, EurophysicsLetters, 9(3), 197-202.

Sornette, A., P. Davy, and D. Sornette (1990) Growth of fractal fault patterns, PhysicalReview Letters, 18(29), 2266-2269.

- 33 -

Thorarinsson, F. (1990) Bouguer density determination by fractal analysis, Geophysics,55(7), 932-935.

Todoeschuck, J. P., and O. G. Jensen (1989) Scaling geometry and seismic deconvolution,Pure and Applied Geophysics, 131(1/2), 273-287.

Turcotte, D. L. (1986) A fractal approach to the relationship between ore grade and tonnage,Economic Geology, 81(6), 1528-1532.

Turcotte, D. L. (1986) A fractal model for crustal deformation, Tectonophysics, 132(1/3),261-269.

Turcotte, D. L. (1986) Fractals and fragmentation, Journal of Geophysical Research,91(B2), 1921-1926.

Turcotte, D. L. (1989) Fractals in geology and geophysics, Pure and AppliedGeophysics, 131(1/2), 171-196.

Turcotte, D.L., R.F. Smalley, and S.A. Solla (1985) Collapse of loaded fractal trees,Nature, 313, 671-672.

Tyler, S. W. (1989) Application of fractal mathematics to soil-water retention estimation, SoilScience Society of America Journal, 53(4), 987-996.

Tyler, S. W., and S. W. Wheatcraft (1990) Fractal processes in soil-water retention, WaterResources Research, 26(5), 1047-1054.

Unwin, D. (1989) Fractals and the geosciences: Introduction, Computers & Geosciences,15(2), 163-166.

Van Damme, H., F. Obrecht, P. Levitz, L. Gatineau and C. Laroche (1986) Fractal viscousfingering in clay slurries, Nature, 320, 731-733.

Wang, J. S. Y., T. N. Narasimhan, and C. H. Scholz (1988) Aperature correlation of a fractalfracture, Journal of Geophysical Research, 93(NB3), 2216-2224.

Whalley, W. B., and J. D. Orford (1982) Analysis of scanning electron microscope images ofsedimentary particle form by fractal dimension and Fourier-analysis methods, ScanningElectron Microscopy, P2, 639-647.

Whalley, W. B., and J. D. Orford (1983) The use of the fractal dimension to characterizeirregular-shaped particles, Sedimentology, 30, 176-194.

Wheatcraft, S. W., and S. W. Tyler (1988) An explanation of scale-dependent dispersivity inheterogeneous aquifers using concepts of fractal geometry, Water ResoucesResearch, 24(4), 566-578.

Willetts, B. (1983) Transport by wind of granular materials of different grain shapes anddensities, Sedimentology, 30, 669-679.

- 34 -

Wong, P.-Z. (1988) The statistical physics of sedimentary rock, Physics Today, 41(12),24-32.

Wong, P.-Z., J. Howard, and J.-S. Lin (1986) Surface roughening and the fractal nature ofrocks, Physical Review Letters, 57(5), 637-640.

Wong, T. F., J. T. Fredrich, and G. D. Gwanesia (1989) Crack aperature statistics and pore-space fractal geometry of westerly granite and rutland quartzite--implications for an elasticcontact model of rock compressibility, Journal of Geophysical Research, 94(NB8),267-278.

Woronow, A. (1981) Morphometric consistency with the Hausdorff-Besicovich dimension,Mathematical Geology, 13(3), 201-216.

Wu, R.-S., K. Aki (1985) The fractal nature of the inhomogeneities in the lithosphereevidenced from seismic wave scattering, Pure and Applied Geophysics, 123, 805-818.

Yamaji, A. (1988) A fractal model for the distribution of stratigraphic hiatuses: A discussion,Journal of Geology, 96(1), 101-102.

Yfantis, E. A., G. T. Flatman, and E. J. England (1988) Simulation of geological surfacesusing fractals, Mathematical Geology, 20(6), 667-672.

Zhao, Z.Y. (1990) Fractal analysis applied to cataclastic rocks, Tectonophysics, 178(214),373-377.

III.10 ECOLOGY/LANDSCAPE

Bak, P., K. Chen, and C. Tang (1990) A forest fire model and some thoughts on turbulence,Physics Letters, 147(4/5), 297-300.

Bradbury, R. H., and R. E. Reichelt (1983) Fractal dimension of a coral reef at ecologicalscales, Marine Ecology Progress Series, 10, 169-171.

Bradbury, R. H., R. E. Reichelt, and D. G. Green (1984) Fractals in ecology: methods andinterpretation, Marine Ecology Progress Series, 14, 295-296.

Dicke, M., and P. A. Burrough (1988) Using fractal dimensions for characterizing tortuosityof animal trails, Physiological Entomology, 13, 393-398.

Frontier, S. (1986) Applications of fractal theory to ecology, in Developments inNumerical Ecology, P. Legendre and L. Legendre, editors, NATA ASI Series G, 14,Springer-Verlag, New York, 335-380.

Gardiner, R. H., B. T. Milne, M. G. Turner, and R. V. O'Neill (1987) Natural models for theanalysis of broad-scale landscape patterns, Landscape Ecology, 1, 5-18.

- 35 -

Haigh, M.H. (1989) Holons, fractals and the dynamics of evolving hierarchical systems, inEcological Principles of Landscape Management and Planning,Proceedings of the CMEH Ecology Summer School, Czechoslovakia, 1988,183-217.

Hastings, H. M., R. Pekelney, R. Monticciolo, D. Vun Kannon, and D. Del Monte (1982)Time scales, persistence and patchiness, BioSystems, 15(4), 281-289.

Kent, C., and J. Wong (1982) An index of littoral zone complexity and its measurement,Canadian Journal of Fisheries and Aquatic Sciences, 39, 847-853.

Krummel, J. P., R. H. Gardner, G. Sugihara, R. V. O'Neill, and P. R. Coleman (1987)Landscape patterns in a disturbed environment, Oikos, 48, 321-324.

Loehle, C. (1983) The fractal dimension and ecology, Speculations in Science andTechnology, 6(2), 131-142.

Logan, B. E., and D. B. Wilkinson (1990) Fractal geometry of marine snow and otherbiological aggregates, Limnology and Oceanography, 35(1), 130-136.

Mark, D. M. (1984) Fractal dimension of a coral reef at ecological scales: a discussion,Marine Ecology - Progress Series, 14, 293-294.

Milne, B. T. (1988) Measuring the fractal geometry of landscapes, Applied Mathematicsand Computation, 27(1), 67-79.

Morse, D. R., J. H. Lawton, M. M. Dodson, and M. H. Williamson (1985) Fractaldimension of vegetation and the distribution of arthropod body lengths, Nature, 314,731-733.

O'Neill, R. V., J. R Krummel, R. H. Gardner, G. Sugihara, B. Jackson, D. L. DeAngelis, B.T. Milne, M. G. Turner, B. Zygmunt, S. W. Christensen, V. H. Dale, and R. L. Graham(1988) Indices of landscape pattern, Landscape Ecology, 1(3), 153-162.

Palmer, M. W. (1988) Fractal geometry: A tool for describing spatial patterns of plantcommunities, Vegetatio, 75, 91-102.

Pennycuick, C. J., and N. C. Kline (1986) Units of measurement for fractal extent, applied tothe coast distribution of bald eagle nests in the Aleutian Islands, Alaska, Oecologia, 68,254-258.

Phillips, J. D. (1985) Measuring complexity of environmental gradients, Vegetatio, 64, 95-102.

Pool, R. (1989) Ecologists flirt with chaos, Science, 243, 310-312.

Ranson, K. J., J. A. Smith, and F. G. Hall (1988) Characterizing forest ecosystem dynamicsthrough modelling and remote sensing observations, Proceedings, InternationalGeoscience and Remote Sensing Symposium (IGARSS), 3, Sept. 12-16,Edinburgh, U.K., European Space Agency publication SP-284, 1347-1350.

- 36 -

Turner, M. G., and C. L. Ruscher (1988) Changes in landscape patterns in Georgia, USA,Landscape Ecology, 1(4), 241-251.

Turner, M. G., R. H. Gardner, V. H. Dale, and R. V. O'Neill (1989) Predicting the spread ofdisturbance across heterogeneous landscapes, Oikos, 55, 121-129.

Vlcek, J., and E. Cheung (1986) Fractal analysis of leaf shapes, Canadian Journal ofForest Research, 16, 124-127.

Warner, W. S., and G. Fry (1990) Evaluating small-format photogrammetry for forest andwildlife surveys - Euclidean and fractal geometry, Forest Ecology and Management,31(1/2), 101-108.

III.11 URBAN STRUCTURES

Arlinghaus, S. L. (1985) Fractals take a central place, Geografiska Annaler, 67B(2), 83-88.

Arlinghaus, S. L., and W. C. Arlinghaus (1989) Fractal theory of central place geometry: ADiophantine analysis of fractal generators for arbitrary Löschian numbers, GeographicalAnalysis, 21(1), 103-121.

Arlinghaus, S. L., and J. D. Nystuen (1990) Geometry of boundary exchanges,Geographical Review, 80(1), 21-31.

Batty, M. (1991) Cities as fractals: simulating growth and form, in R. Earnshaw et al.,editors, Fractals and Chaos, Springer Verlag, New York, in press.

Batty, M. (1991) Generating urban forms from diffusive growth, Environment andPlanning A, 22, in press.

Batty, J. M., A. S. Fotheringham, and P. A. Longley (1989) Urban growth and form:scaling, fractal geometry and diffusion-limited aggregation, Environment andPlanning A, 21(11), 1447-1472.

Batty, J. M., and P. A. Longley (1986) The fractal simulation of urban simulation,Environment and Planning A, 18(9), 1143-1179.

Batty, J. M., and P. A. Longley (1987) Fractal-based description of urban form,Environment and Planning B, 14(2), 123-134.

Batty, J. M., and P. A. Longley (1987) Urban shapes as fractals, Area, 19(3), 215-221.

Batty, J. M., and P. A. Longley (1988) The morphology of urban land use, Environmentand Planning B, 15, 461-488.

Dutton, G. (1973) Criteria of growth in urban systems, Ekistics, 215, 298-307.

- 37 -

Fotheringham, A. S., M. Batty, and P. A. Longley (1989) Diffusion-limited aggregation andthe fractal nature of urban growth, Papers of the Regional Science Association,67, 55-69.

Laurini, R., and F. Milleret (1987) Les relations de Peano dans les bases de donnéesgéographiques, Symposium Proceedings, Geomatics Applied to MunicipalManagement, Nov. 4-6, Montreal, Quebec, 65-78.

Longley, P. A., and M. Batty (1989) On the fractal measurement of geographical boundaries,Geographical Analysis, 21(1), 47-67.

Wong, D. W. S., and A. S. Fotheringham (1990) Urban systems as examples of boundedchaos: Exploring the relationship between fractal dimension, rank-size, and rural-to-urbanmigration, Geografiska Annaler, in press.

III.12 HUMAN GEOGRAPHY

Allen, P. M., and J. M. McGlade (1987) Modelling complex human systems: A fisheriesexample, European Journal of Operational Research, 30, 147-167.

Kelsey, D. (1988) The economics of chaos or the chaos of economics, Oxford EconomicPapers, 40, 1-31.

III.13 REMOTE SENSING

De Cola, L. (1989) Fractal analysis of a classified Landsat scene, PhotogrammetricEngineering and Remote Sensing, 55(5), 601-610.

De Cola, L. (1989) Pareto and fractal descriptions of regions from a binomial lattice,Geographical Analysis, 21(1), 74-81.

Dellepiane, S., D. D. Giusto, S. B. Serpico, and G. Vernazza (1988) Information fusion by aknowledge-based system for SAR image interpretation, Proceedings, InternationalGeoscience and Remote Sensing Symposium (IGARSS), 3, Sept. 12-16,Edinburgh, U.K., European Space Agency publication SP-284, 1845-1846.

Dellepiane, S., S. B. Serpico, and G. Vernazza (1988) Analysis and classification of SARimages by a knowledge-based approach, Proceedings, 9th InternationalConference on Pattern Recognition, II, Nov. 17-19, Rome, 1207-1209.

Gabriel, P., S. Lovejoy, D. Schertzer, and G. L. Austin (1988) Multifractal analysis ofresolution dependence in satellite imagery, Geophysical Research Letters, 15(12),1373-1376.

- 38 -

Harger, R. O. (1990) SAR object detection with fractal terrain models, Proceedings,International Geoscience and Remote Sensing Symposium (IGARSS'90), I,May 20-24, College Park, Maryland, 313-316.

Jones, J. G., and R. W. Thomas (1985) A statistical model for localised natural features inmeasured satellite imagery, in Digital Signal Processing - 84, in V. Cappellini andA.G. Constantinides, editors, Elsevier, New York, 638-643.

Jones, J. G., R. W. Thomas, and P. G. Earwicker (1989) Fractal properties of computer-generated and natural geophysical data, Computers & Geosciences, 15(2), 227-235.

Kubik, K., and F. Leberl (1986) Fractal behavior of terrain topography, Proccedings,Technical Papers of the 52nd Annual Meeting of the American Society ofPhotogrammetry and Remote Sensing, 4, Washington, D.C., 187-190.

Lam, N. S.-N. (1990) Description and measurement of Landsat TM images using fractals,Photogrammetric Engineering and Remote Sensing, 56(2), 187-192.

Longley, P. A., M. Batty, and J. Shepherd (1991) The size, shape and dimension of urbansettlements, Transactions of the Institute of British Geographers, in press.

Lovejoy, S., and D. Schertzer (1988) Extreme variability scale invariance and fractals inremote sensing: analysis and simulation, in Digital Image Processing in RemoteSensing, D. Muller, editor, Francis and Taylor, London, 177-212.

MacLennan, M. J., and P. J. Howarth (1987) The use of fractal geometry to identify ranges ofscale-invariance in digital remotely sensed data, Proceedings, Twenty-FirstInternational Symposium on Remote Sensing of Environment, 2, Oct. 26-30,Ann Arbor, Michigan, 1089-1092.

Pendock, N. (1985) Fast classification of image data with large spectral dimension,Proceedings, Nineteenth International Symposium on Remote Sensing ofEnvironment, Oct. 21-25, Ann Arbor, Michigan, 281-285.

Ramstein, G., and M. Raffy (1989) Analysis of the structure of remotely-sensed images,International Journal of Remote Sensing, 10, 1049-1073.

Ramstein, G., and M. Raffy (1990) Algorithme d'analyse fractale de contours en télédétectionet applications, International Journal of Remote Sensing, 11(2), 191-208.

III.14 IMAGE COMPRESSION

Barnsley, M. F., and J. Elton (1988) A new class of Markov processes for image encoding,Journal of Applied Probability, 20(1), 14-32.

Barnsley, M. F., and A. E. Jacquin (1988) Application of recurrent iterated function systemsto images, Visual Communications and Image Processing'88, Proceedings ofSPIE, 1001, Nov. 9-11, Cambridge, Massachusetts, 122-131.

- 39 -

Barnsley, M. F., and A. D. Sloan (1987) Chaotic compression, Computer GraphicsWorld, 10(11), 107-108.

Barnsley, M. F., and A. D. Sloan (1988) A better way to compress images, BYTE, 13(1),215-223.

Barnsley, M. F., and A. D. Sloan (1989) Fractal image compression, Proceedings,Scientific Data Compression Workshop, NASA Goddard Space Flight Center,Greenbelt, Maryland, 351-365.

Bell, S. B. M., B. M. Diaz, F. Holroyd, and M. J. Jackson (1983) Spatially referencedmethods of processing raster and vector data, Image and Vision Computing, 1(4),211-220.

Cipra, B. A. (1989) Image captured by computer, Science, 243, 1288-1289.

Giusto, D. D., C. S. Regazzoni, S. B. Serpico, and G. Vernazza (1989) High-performanceimage coding. Integration of different technologies by a knowledge-based recognitionsystem, Alta Frequenza, 58(3), 277-285.

Goel, B. D., and S. C. Kwatra (1988) A data-compression algorithm for color images basedon run-length coding and fractal geometry, in Proceedings, IEEE InternationalConference on Communications'88: Digital Technology: Spanning theUniverse, 2, June 12-15, Philadelphia, 1253-1256.

Kandebo, S. W. (1988) Fractals research furthers digitized image compression, AviationWeek & Space Technology, 128(17), 91-95.

Kocsis, S. M. (1989) Fractal-based image compression, in Twenty-Third AsilomarConference on Signals, Systems & Computers: Converence Record, 1, R.R.Chen, editor, Maple Press, Santa Clara, California, 177-181.

Marbach, W. D. (1989) Geometry could give HDTV signals the right shape, BusinessWeek, April 3, 110.

Ojha, P. (1989) Fractals shorten the lines for transmitting videos, New Scientist,124(1689), 40.

Reddaway, S. F., A. Wilson and A. Horn (1988) Fractal graphics and image compression ona SIMD Processor, Proceedings, The Second Symposium on the Frontiers ofMassively Parallel Computations, Oct. 10-12, Fairfax, Virginia, IEEE, 265-274.

Reuter, L. (1987) Rendering and Magnification of Fractals Using InteratedFunction Systems. Unpublished PhD Thesis, Georgia Institute of Technology.

Stevens, R. J., A. F. Lehar, and F. H. Preston (1983) Manipulation and presentation ofmultidimension Data using the Peano scan, IEEE Transactions on Pattern Analysisand Machine Intelligence, 5(5), 520-526.

Walach, E., and E. Karnin (1986) A fractal based approach to image compression, IEEE-IECEJ-ASJ International Conference on Acoustics, Speech and SignalProcessing (ICASSP 86 Proceedings), I, April 7-11, Tokyo, Japan, 529-532.

- 40 -

Walach, E., E. Karnin, and D. Chevion (1986) On fractal based approach to image coding, inSignal Processing III: Theories and Applications, Part 2, I. T. Young, R. P. W.Duin, J. Biemond, and J. J. Gerbrands, editors, North-Holland, Amsterdam, 731-734.

Waters, T. (1989) Fractals in your future, Discover, 10(3), 26-28.

III.15 IMAGE PROCESSING

Aitkheddache, A., and S. A. Rajala (1988) Texture classification based on higher-orderfractals, International Conference on Acoustics, Speech and SignalProcessing, (ICASSP'88), April, New York, IEEE, 1112-1115.

Berger, M. A. (1989) Images generated by orbits of 2-D Markov chains, Change: NewDirections for Statistics and Computing, 2(2), 18-28.

Brammer, R. F. (1988) Application of fractals and chaos modeling in visual computing,Visual Communications and Image Processing'88, Proceedings of SPIE, 1001,Nov. 9-11, Cambridge, Massachusetts, 78-86.

Brammer, R. F. (1989) Unified image computing based on fractals and chaos modeltechniques, Optical Engineering, 28(7), 726-734.

Chang, C., and S. Chatterjee (1989) Fractal based approach to shape-description,reconstruction and classification, in Twenty-Third Asilomar Conference onSignals, Systems & Computers: Converence Record, 1, R.R. Chen , editor,Maple Press, Santa Clara, California, 172-176.

Chen, C. C., J. S. Daponte, and M. D. Fox (1989) Fractal feature analysis and classificationin medical imaging, IEEE Transactions on Medical Imaging, 8(2), 133-142.

Chen, S. S., J. M. Keller, and R. M. Crownover (1990) Shape from fractal geometry,Artificial Intelligence, 43(2), 199-218.

Chermant, J. L., and M. Coster (1978) Fractal object in image analysis, Proceedings,International Symposium on Quantitative Metallography, November 21-23,Florence, Italy, Associazione Italiana de Metallurgia, 125-138.

Cipra, B. A. (1989) Image capture by computer, Research News, 243, 1288-1289.

Dambra, C., S. Dellepiane, C. Regazzoni, S. B. Serpico, and G. Vernazza (1988) Textureanalysis of 3D objects by a fractal-preserving approach, Visual Communications andImage Processing'88, Proceedings of SPIE, 1001, Nov. 9-11, Cambridge,Massachusetts, 732-738.

Davidson, J. A. (1985) The measurement of image sharpness through the approaches used todescribe fractals, Society of Motion Picture and Television Engineers Journal,94(8), 802-809.

- 41 -

Dellepiane, S., S. B. Serpico, G. Vernazza, and R. Viviani (1987) Fractal-based image-analysis in radiological applications, Visual Communications and ImageProcessing II, Proceedings of SPIE, 845, 396-403.

Dennis, T. J., and N. G. Dessipris (1989) Fractal modeling in image texture analysis, IEEProceedings-F Radar and Signal Processing, 136(5), 227-235.

Dodd, N. A. (1986) Texture generation using fractal concepts, Second InternationalConference on Image Processing and its Applications, June 24-26, London,U.K., 251-257.

Dodd, N. A. (1987) Multispectral texture synthesis using fractal concepts, IEEETransactions on Pattern Analysis and Machine Intelligence, 9(5), 703-707.

Dodds, D. R. (1988) Fractals, fuzzy-sets and image representation, VisualCommunications and Image Processing'88, Proceedings of SPIE, 1001, Nov. 9-11, Cambridge, Massachusetts, 87-94.

Fortin, C. S., W. J. Ohley, and H. Gerwirtz (1990) Fractal dimension as a method ofsegmenting cardiac images, Proceedings, Sixteenth Annual NortheastBioengineering Conference, March 26-27, State College, Pennsylvania, 45-48.

Hanson, B., and Y. Y. Zeevi (1987) A pyramid of image generating functions, VisualCommunications and Image Processing II, Proceedings of SPIE, 845, 253-257.

Keller, J. M., and T. Downey (1988) Fuzzy segmentation of natural scenes using fractalgeometry, Intelligent robots and computer vision, Proceedings of SPIE, 1002,369-376.

Keller, J. M., S. Chen., and R. M. Crownover (1989) Texture description and segmentationthrough fractal geometry, Computer Vision, Graphics and Image Processing,45(2), 150-166.

Kube, P., and A. Pentland (1988) On the imaging of fractal surfaces, IEEE Transactionson Pattern Analysis and Machine Intelligence, 10(5),704-707.

Kublinski, W. S. (1987) Utilization of spatial self-similarity in medical image processing,Medical Imaging, Proceedings of SPIE, 767, 346-351.

Lalitha, L., and D. D. Majumder (1989) Fractal based criteria to evaluate the performance ofdigital image magnification techniques, Pattern Recognition Letters, 9(1), 67-75.

Lundahl, T., W. J. Ohley, W. S. Kuklinski, D. O. Williams, H. Gewirtz, and A. S. Most(1985) Analysis and interpolation of angiographic images by use of fractals, IEEEComputers in Cardiology, September 8-11, Linkoping, Sweden, 355-357.

Lundahl, T., W. J. Ohley, S. M. Kay, and R. Siffert (1986) Fractional Brownian motion: Amaximum likelihood estimator and its application to image texture, IEEE Transactionson Medical Imaging, 5(3), 152-161.

- 42 -

Medioni, G., and Y. Yasumoto (1984) A note on using the fractal dimension forsegmentation, Proceedings of the Workshop on Computer VisionRepresentation and Control, April 30-May 2, Annapolis, Maryland, 25-30.

Mussingmann, U., M. Rueff, and M. Schmutz (1987) Fractal based algorithms for textureanalysis, Automated Inspection and High Speed Vision Architectures,Proceedings of SPIE, 489, 109-116.

Nguyen, P. T., and J. Quinqueton (1982) Space filling curves and texture analysis,Proceedings of the Sixth International Conference on Pattern Recognition,Oct. 19-22, Munich, Germany, 282-285.

Normand, M. D., and M. Peleg (1986) Determination of the fractal dimension of a particlesilhouette using image-processing techniques, Powder Technology, 45, 271-275.

Ohley, W. J., and T. Lundahl (1987) Discrete two-dimensional fractional Brownian motion asa model for medical images, Visual Communications and Image Processing II,Proceedings of SPIE, 845, 227-232.

Peleg, S., J. Noar, R. Hartley, and D. Avnir (1984) Multiple resolution texture analysis andclassification, IEEE Transactions on Pattern Analysis and MachineIntelligence, 6(4), 518-523.

Peli, T., V. Tom, and B. Lee (1989) Multiscale fractal and correlation signatures for imagescreening and natural cluster suppression, Visual Communications and ImageProcessing, Proceedings of SPIE, 1199, Nov. 8-10, Philadelphia, Pennslyvania, 402-415.

Peli, T. (1990) Multiscale fractal theory and object characterization, Journal of the OpticalSociety of America A - Optics and Image Science, 7(6), 1101-1112.

Pentland, A. P. (1983) Fractal texture, Proceedings, International Joint Conferenceon Artificial Intelligence (IJCAI), August, Karlsruhe, Germany, 973-981.

Pentland, A. P. (1984) Fractal-based description of natural scenes, IEEE Transactions onPattern Analysis and Machine Intelligence, 6(6), 661-674.

Pentland, A. P. (1985) On describing complex surfaces, Image and Vision Computing,3(4), 153-162.

Pentland, A. P. (1986) Perceptual organization and the representation of natural form,Artificial Intelligence, 28, 293-331.

Pentland, A. P. (1986) Shading into texture, Proceedings, National Conference onArtificial Intelligence, August 6-10, Austin, Texas, 269-273.

Pentland, A. P. (1986) Shading into texture, Artificial Intelligence, 29(1), 147-170.

Pentland, A. P. (1986) Shading into texture, in From Pixels to Predicates, A.P.Pentland, editor, Ablex Publishing, Norwood, New Jersey, 253-267.

- 43 -

Pentland, A. P. (1987) Fractal surface models for communication about terrain, VisualCommunications and Image Processing II, Proceedings of SPIE, 845, 301-307.

Rigaut, J. P. (1987) Natural objects show fractal gray tone functions - a novel approach toautomated image segmentation using mathematical morphology, Acta Stereologica, 6,supplement 3, parts 1-2, 799-802.

Rigaut, J. P. (1988) Automated image segmentation by mathematical morphology and fractalgeometry, Journal of Microscopy, 150, 21-30.

Rueff, M. (1988) Can scale space filtering enhance fractal analysis?, Intelligent Robotsand Computer Vision, Proceedings of SPIE, 1002, 136-143.

Simon, J. C., and J. Quinqueton (1980) On the use of a peano scanning in image processing,in Issues in Digital Image Processing, R.M. Haralick and J.C. Simon, editors,Sijthoff & Noordhoff, Germantown, Maryland, 357-366.

Strahle, W. C. (1988) Adaptive nonlinear filter using fractal geometry, Electronics Letters,24(19), 1248-1249.

Stein, M. C. (1987) Fractal image-models and object detection, Visual Communicationsand Image Processing II, Proceedings of SPIE, 845, 293-300.

Stevens, R. J., A. F. Lehar, and F. H. Preston (1983) Manipulation and presentation ofmultidimension Data using the Peano scan, IEEE Transactions on Pattern Analysisand Machine Intelligence, 5, 520-526.

Szeliski, R. (1987) Regularization using fractal priors, Proceedings, AmericanAssociation of Artificial Intelligence (AAAI'87), 2, Seattle, Washington, 749-754.

Thornton, J. I. (1986) Fractal surfaces as models of physical matches, Journal of theForensic Science Society, 31(4), 1435-1438.

Tricot, C., D. Wehbi, J. F. Quiniou, and C. Roquescarmes (1987) Concepts of non-integerdimension applied to image treatment, Acta Stereologica, 6, supplement 3, parts 1-2,839-844.

Walach, E., E. Karnin, and D. Chevion (1986) On fractal based approach to image coding, inSignal Processing III: Theories and Applications, Part 2, I. T. Young, R. P. W.Duin, J. Biemond and J. J. Gerbrands, editors, North-Holland, Amsterdam, 731-734.

Williams, P. K., D. G. Lubnau, and D. F. Elliott (1988) Generation of fractal images andcomparison of their PSDs with several models, Proceedings, Twenty-SecondAsilomar Conference on Signals, Systems & Computers, Oct. 31-Nov. 2,Pacific Grove, California, 495-499.

Wiseman, N. E., and S. Nedunuri (1986) Computing random fields, The ComputerJournal, 29(4), 373-377.

- 44 -

Yang, K.-M., L. Wu, and M. Mills (1988) Fractal based coding scheme using Peano scan,Proceedings, IEEE International Symposium on Circuits and Systems, June7-9, Espoo, Finland, 2301-2304.

Zhang, P., H. Barad, and A. Martinez (1989) Fractal-based pattern-recognition and itsapplications to cell image-analysis, Visual Communications and ImageProcessing, Proceedings of SPIE, 1199, Nov. 8-10, Philadelphia, 896-902.

III.16 FRACTAL SYNTHESIS

Barnsley, M. F. (1988) Fractal modeling of real world images, in The Science of FractalImages, H.-O. Peitgen and D. Saupe, editors, Springer-Verlag, New York, 219-242.

Barnsley, M. F., A. Jacquin, F. Malassent, L. Reuter, and A. D. Sloan (1988) Harnessingchaos for image synthesis, Computer Graphics, 22(4), 131-140.

Beyer, T., and M. Friedell (1987) Generative scene modelling, Proceedings,Eurographics'87, North-Holland, Amsterdam, 151-158.

Bouville, C. (1985) Bounding ellipsoids for ray-fractal intersection, Computer Graphics,19(3), 45-52.

Ciarcia, C. (1990) Creating fractal images, Circuit Cellar INK, 17, 24-37.

Clarke, K. C. (1987) Scale-based simulation of topography, Proceedings, EighthInternational Symosium on Computer-Assisted Cartography (AUTO-CARTO 8), March 29-April 3, Baltimore, Maryland, 680-688.

Clarke, K. C. (1988) Scale-based simulation of topographic relief, The AmericanCartographer, 15(2), 173-181

Demko, S., L. Hodges, and B. Naylor (1985) Construction of fractal objects with iteratedfunction systems, Computer Graphics, 19(3), 271-278.

Doerer, D. M., and C. L. Sabharwal (1989) New twist to fractals, Proceedings,Seventeenth Annual ACM Computer Science Symposium Conference, Feb.21-23, Louisville, Kentucky, 145-155.

Edwards, G. J. (1984) Fractal based terrain modelling, Proceedings, Conference onComputer Animation and Digital Effects, October, London, 49-56.

Estvanik, S. (1986) From fractals to graftals, Computer Language, March, 3(7), 45-48.

Falcidienco, B., and C. Pienovi (1990) Natural surface approximation by constrainedstochastic interpolation, Computer-Aided Design, 22(3), 167-172.

Fellous, A., J. Granara and J. Hourcade (1985) Fractional Brownian relief: an exact localmethod, in Proceedings of Eurographics'85, North Holland, New York, 353-363.

- 45 -

Finlay, W. M. (1987) Fractal terrain image synthesis for simulation using Defense MappingAgency data, Infrared Image Processing and Enhancement, Proceedings of SPIE,781, May 20-21, Orlando, Florida, 58-62.

Fournier, A. (1980) Stochastic Modeling in Computer Graphics. PhD dissertation,University of Texas, Dallas.

Fournier, A., and D. Fussell (1980) Stochastic modelling in computer graphics, ComputerGraphics, 14(6), 1-14.

Fournier, A., D. Fussell, and L. Carpenter (1982) Computer rendering of stochastic models,Communications of the ACM, 25(6), 371-384.

Fournier, A., D. Fussell, and L. Carpenter (1982) Author's rely to comments on computerrendering of fractal stochastic models by B. B. Mandelbrot, Communications of theACM, 25(8), 583-584.

Fournier, A., and T. Milligan (1985) Frame buffer algorithms for stochastic models, IEEEComputer Graphics and Applications, 5(10), 40-46.

Fox, C. G. (1987) An inverse Fourier transform algorithm for generating random signals of aspecified spectral form, Computers & Geosciences, 13(4), 369-374.

Herbert, F. (1984) Fractal landscape modelling using octrees, IEEE Computer Graphicsand Applications, 4, 4-5.

Horgan, J. (1988) Fractal shorthand, Scientific American, 258(2), 28.

Jeffrey, T. (1987) Mimicking mountains, BYTE, 12(12), 337-338,340,342,344.

Lévesque, M. P. (1987) Simulation of aerial imagery, Proceedings, Summer ComputerSimulation Conference, July 27-30, Montreal, The Society for Computer Simulation,745-748.

Lewis, J. P. (1986) Methods for stochastic spectral synthesis, Proceedings, GraphicsInterface'86/Vision Interface'86, May 26-30, Vancouver, British Columbia, 173-179.

Lewis, J. P. (1987) Generalized stochastic subdivision, ACM Transactions onGraphics, 6(3), 167-190.

Mandelbrot, B. B. (1982) Comment on computer rendering of fractal stochastic models,Communications of the ACM, 25(8), 581-584.

Mandelbrot, B. B. (1988) Fractal landscapes without creases and with rivers, in TheScience of Fractal Images, H.-O. Peitgen and D. Saupe, editors, Springer-Verlag,New York, 243-260.

Miller, G. S. P. (1986) The definition and rendering of terrain maps, Computer Graphics,20(4), 39-48.

- 46 -

Norton, A. (1982) Generation and display of geometric fractals in 3-D, ComputerGraphics, 16(3), 61-66.

Oppenheimer, P. (1986) Fractals, computers and DNA, Proceedings, GraphicsInterface'86/Vision Interface'86, May 26-30, Vancouver, British Columbia, 254-258.

Pentland, A. P. (1986) Parts: Structured description of shape, Proceedings, FifthNational Conference on Artificial Intelligence (AAAI-86), 1, Aug. 11-15,Philadelphia, 695-701.

Pentland, A. P. (1986) Part structure for 3-D sketching, Proceedings, GraphicsInterface'86/Vision Interface'86, May 26-30, Vancouver, British Columbia, 223-228.

Prusinkiewicz, P. (1986) Graphical applications of L-systems, Proceedings of GraphicsInterface '86, 26-30 May.

Reeves, W. T., and R. Blau (1985) Approximate and probabilistic algorithms for shading andrendering structured particle systems, Computer Graphics, 19(3), 313-322.

Schmitt, G. (1988) Expert systems and interactive fractal generators in design and evaluation,in CAAD Futures'87, T. Maver and H. Wagter, editors, Elsevier, Amsterdam, 91-106.

Smith, A. R. (1982) The genesis demo: instant evolution with computer graphics, AmericanCinematographer, 63, 1038-1039, 1048-1050.

Smith, A. R. (1984) Plants, fractals, and formal languages, Computer Graphics, 18(3), 1-10.

Stepoway, S. L., and M. Christiansen (1988) Parallel rendering of fractal surfaces,International Journal of Parallel Programming, 17(1), 43-58.

Stepoway, S. L., and M. Christiansen (1989) Object-oriented fractal modeling on a shared-memory MIMD machine, Journal of Object-Oriented Programming, 2(1), 20-25.

Vandepanne, M. (1985) 3-D fractals, Creative Computing, 11(7), 78-82.

Voss, R. (1985) Random fractal forgeries, in Fundamental Algorithms for ComputerGraphics, R.A. Earnshaw, editor, NATO ASI Series F, 17, Springer-Verlag, NewYork, 805-835.

Voss, R. (1985) Random fractal forgeries: From mountains to music, in Science andUncertainty, S. Nash, editor, Science Reviews Ltd., Middlesex, England, 69-85.

Willers, C. J. (1988) Applications of fractal geometry to modelling nature, Proceedings,South African Conference on Communications and Signal Processing(COMSIG 88), June 24, Pretoria, IEEE, 123-129.

- 47 -

Wyvill, B., C. McPheeters, and M. Novacek (1985) Specifying stochastic objects in ahierarchical graphics system, Proceedings, Graphics Interface'85, May 27-31,Montreal, Quebec, 17-20.

IV. MISCELLANEOUS

Adler, R. J. (1978) Some erratic patterns generated by the planar Wiener process,Supplement, Advances in Applied Probability, 10, 22-27.

Aharony, A. (1984) Percolation, fractals, and anomalous diffusion, Journal of StatisticalPhysics, 34, 931-939.

Avnir, D., and P. Pfeifer (1983) Fractal dimension in chemistry: an intensive characteristic ofsurface irregularity, Nouveau Journal de Chemie, 7(2), 71-72.

Avnir, D., D. Farin, and P. Pfeifer (1984) Molecular fractal surfaces, Nature, 308(15), 261-263.

Avnir, D., D. Farin, and P. Pfeifer (1985) Surface geometric irregularity of particulatematerials: the fractal approach, Journal of Colloid and Interface Science, 103(1),112-123.

Bak, P., C. Tang and K. Wiesenfeld (1988) Self-organized criticality, Physical Review A,38(1), 364-374.

Bak, P., and K. Chan (1991) Self-organized criticality, Scientific American, 264(1). 46-53.

Ball, R. C., M. J. Blunt, and O. R. Spivack (1988) Diffusion-controlled growth,Proceedings of the Royal Society of London, Series A, 423(1864), 123-132.

Banavar, J. R., M. Muthukumar, and J. F. Willemsen (1985) Fractal geometries in decaymodels, The Institute of Physics, 18, 16-65.

Bedrosian, S. D., and D.L.Jaggard (1987) A fractal-graph approach to large networks,Proceedings of the IEEE, 75(7), 966-968.

Ben-Jacob, E., N. Goldenfeld, J. S. Langer and G. Schon (1983) Dynamics of interfacialpattern formation, Physical Review Letters, 51, 21, 1930-1932.

Ben-Jacob, E., G. Deutscher, P. Garik, N. D. Goldenfeld, and Y. Lareah (1986) Formationof a dense branching morphology in interfacial growth, Physical Review Letters, 57,15, 1903-1906.

Berry, M.V. (1979) Diffractals, Journal of Physics A, 12, 781-797.

Broomhead, D.S., and R. Jones (1988) Time-series analysis, Proceedings of the RoyalSociety of London, Series A, 423(1864), 103-121.

- 48 -

Camacho, C. J., and M. E. Fisher (1990) Tunable fractal shapes in self-avoiding polygonsand planar vesicles, Physical Review Letters, 65(1), 9-12.

Chen, J.-D., and D. Wilkinson (1985) Pore-scale viscous fingering in porous media,Physical Review Letters, 55, 18, 1892-1895.

Clark, N. N. (1985) Three techniques for implementing digital fractal analysis of particleshape, Powder Technology, 46(1), 45-52.

Dreiling, L. (1986) Fractal art -the power of computer graphics images, ComputerGraphics World, 9(7), 91-92.

Ensor, D. S., and M. E. Mullins (1985) The fractal nature of dendrites formed by thecollection of particles on fibers, Particle Characterisation, 2, 77-78.

Flook, A. G. (1978) The use of dilation logic on the quantimet to achieve fractal dimensioncharacterization of textured and structured profiles, Powder Technology, 21, 295-298.

Forrest, S. R., and T. A. Witten Jr. (1979) Long-range correlations in smoke-particleaggregates, Journal of Physics A, 12(5), L109-L117.

Gould, H., Fereydoon Family, and H. E. Stanley (1983) Kinetics of formulation of randomlybranched aggregates: a renormalization-group approach, Physical Review Letters,50(9), 686-689.

Grassberger , P. (1985) On the spreading of two-dimensional percolation, Journal ofPhysics A, 18, L215-L219.

Grossman, S., F. Wegener, and K. H. Hoffman (1985) Anomalous diffusion on a self-similar hierarchical structure, Le Journal De Physique - Lettres, 46(13), 575-583.

Halsey, T. C., P. Meakin, and I. Procaccia (1986) Scaling structure of the surface layer ofdiffusion-limited aggregates, Physical Review Letters, 56(8), 854-857.

Honda, H. (1971) Description of the form of trees by the parameters of the tree-like body:effects of the branching angle and the branch length on the shape of the tree-like body,Journal of Theoretical Biology, 31, 331-338.

Honda, H., P. B. Tomlinson, and J. B. Fisher (1982) Two geometrical models of branchingof botanical trees, Annals of Botany, 49, 1-11.

Honda, H. (1985) Branching structures of trees in three dimensions, Science on Form, 1,85-94.

Honjo, H., S. Ohta, and Y. Sawada (1985) New experimental findings in two-dimensionaldendritic crystal growth, Physical Review Letters, 55(8), 841-844.

Hughes, B. D., E. W., Montroll and M. F. Shlesinger (1982) Fractal random walks,Journal of Statistical Physics, 28, 111-126.

- 49 -

Hurd, A. J., and D. W. Schaefer (1985) Diffusion-limited aggregation in two dimensions,Physical Review Letters, 54(10), 1043-1046.

Jakeman, E., and D. L. Jordan (1990) Statistical accuracy of measurements on Gaussianrandom fields, Journal of Physics D, 23(4), 397-405.

Kadanoff, L.P. (1989) Fractals and multifractals in avalanche models, Physica D, 38(1/3),213-214.

Katz, M. J., and E. B. George (1985) Fractals and the analysis of growth paths, Bulletin ofMathematical Biology, 47(2), 173-286.

Kaye, B. H. (1978) Specification of the ruggedness and/or texture of a fine particle profile byits fractal dimension, Powder Technology, 21, 1-16.

Kaye, B. H. (1984) Multifractal description of a rugged fineparticle profile, ParticleCharacterization, 11, 14-21.

Kaye, B. H., J. E. Leblanc, and P. Abbot (1985) Fractal description of the structure of freshand eroded aluminum shot fineparticles, Particle Characterization, 2, 56-61.

Kaye, B. H. (1986) The description of 2 dimensional rugged boundaries in fine particlescience by means of fractal dimensions, Powder Technology, 46, 245-254.

King, B. B., L.J. Weissman, and J.B. Bassingthwaighte (1990) Fractal descriptions forspatial statistics, Annals of Biomedical Engineering, 18(2), 111-121.

Kolb, M. (1987) Anisotropic diffusion limited aggregation: from self-similarity to self-affinity,Europhysics Letters, 4(1), 85-90.

Kondo, H., M. Matsushita, and S. Ohnishi (1986) Diffusion-limited aggregation with arestriction of growth direction, in Science on Form: Proceedings of the FirstInternational Symposium for Science on Form,Y. Kato, R. Takaki and J.Toriwaki , editors, KTK Scientific, Tokyo, 33-38.

Langer, J. S. (1989) Dendrites, viscous fingers, and the theory of pattern formation,Science, 243, 1150-1156.

Lenormand, R. (1988) Flow through porous media: limits of fractal patterns, Proceedings ofthe Royal Society of London, Series A, 423(1864), 159-168.

Lew, R. R., and C.L. Scharf (1990) Fractal filling of channel data, Biochimica etBiophysica Acta, 1023(2), 305-311.

Louis, E., F. Guinea, and F. Flores (1986) The fractal nature of facture, in Fractals inPhysics, L. Pietronero and E. Tosatti, editors, Elsevier, New York, 177-180.

Maloy, K. J., J. Feder, and T. Jossang (1985) Viscous fingering fractals in porous media,Physical Review Letters, 55, 2688-2691.

Mandelbrot, B. B. (1978) Getting snowflakes into shape, New Scientist, 78(1108), 808-810.

- 50 -

Mandelbrot , B. B. (1984) Each fractal set has a unique fractal dimension, in Turbulenceand Chaotic Phenomena in Fluids, T. Tatsumi , editor, Elsevier, New York, 203-208.

Mandelbrot, B.B. (1990) Negative fractal dimensions and multifractals, Physics A, 163,306-315.

Mandelbrot , B. B., and J. A. Given (1984) Physical properties of a new fractal model ofpercolation clusters, Physical Review Letters, 52(21), 1853-1856.

Mandelbrot , B. B., D. E. Passoja, and A. J. Paullay (1984) Fractal character of fracturesurfaces of metals, Nature, 19, 721-722.

Mann, R. and M. C. Wasilowski (1990) Towards a fractal computer graphics basis forcharacterization of catalyst pore structure by image-reconstruction, ChemicalEngineering Research and Design, 68(2), 177-184.

Martin, J. E. (1985) Topological and geometrical properties of random fractals, Journal ofPhysics A, 18, L207-L214.

Matsushita, M., Y. Hayakawa, K. Sumida, and Y. Sawada (1986) Experimentalinvestigations on the fractality and kinetics of aggregation, in Science on Form:Proceedings of the First International Symposium for Science on Form, Y.Kato, R. Takaki and J. Toriwaki, editors, KTK Scientific, Tokyo, 23-31.

Mazel, D.S., and M.H. Hayes (1989) Fractal modeling of time-series data, Twenty-ThirdAsilomar Conference on Signals, Systems & Computers: ConverenceRecord, 1, R.R. Chen, editor, Maple Press, Santa Clara, California, 182-186.

Meakin, P. (1983) Cluster-growth processes on a two-dimensional lattice, Physical ReviewB, 28(12), 6718-6732.

Meakin, P. (1983) Diffusion-controlled cluster formation in 2-6 dimensional space, PhysicalReview A, 27(3), 1495-1507.

Meakin, P. (1983) Diffusion-controlled cluster formation in two, three and four dimensions,Physical Review A, 27(1), 604-607.

Meakin, P. (1983) Diffusion-controlled deposition on fibers and surfaces, Physical ReviewA, 27(5), 2616-2623.

Meakin, P., and S. Tolman (1988) Diffusion-limited aggregation, Proceedings of theRoyal Society of London, Series A, 423(1864), 133-148.

Meakin, P., and T. A. Witten, Jr. (1983) Growing interface in diffusion-limited aggregation,Physical Review A, 28(5), 2985-2989.

Meakin, P. (1986) A new model for biological pattern formation, Biological PatternFormation, 118, 101-113.

- 51 -

Meakin, P. (1986) Multiple-contact diffusion-limited-aggregation model, Physical ReviewA, 33(6), 4199-4204.

Meakin, P. (1986) Universality, nonuniversality, and the effects of anisotropy on diffusion-limited aggregation, Physical Review A, 33(5), 3371-3382.

Meakin, P. (1987) Diffusion-limited aggregation on multifractal lattices: a model for fluid-fluiddisplacement in porous media, Physical Review A, 36(6), 2833-2837.

Muthukumar, M. (1983) Mean-field theory for diffusion-limited cluster formation, PhysicalReview Letters, 50(11), 839-842.

Nagatani, T. (1987) A hierarchical model for scaling structure in generalised diffusion-limitedaggregations, Journal of Physics A, 20, L641-L647.

Nagatani, T. (1987) Renormalization-group approach to multifractal structure of growthprobability distribution in diffusion-limited aggregation, Physical Review A, 36(12),5812-5819.

Nakamura, M. (1990) Self-affine fractal dimensions of film surfaces, Physical Review B,41(17), 2268-2269.

Niemeyer, L., L. Pietronero, and H. J. Wiesmann (1984) Fractal dimension of dielectricbreakdown, Physical Review Letters, 52(12), 1033-1036.

Nittmann, J., G. Daccord, and H. E. Stanley (1985) Fractal growth of viscous fingers:quantitative characterization of a fluid instability phenomenon, Nature, 314, 141-145.

Orbach, R. (1986) Dynamics of fractal networks, Science, 231, 814-819.

Oxaal, U., M. Murat, F. Boger, A. Aharony, J. Feder, and T. Jossang (1987) Viscousfingering on percolation clusters, Nature, 329, 32-37.

Packard, N. H. (1986) Lattice models for solidification and aggregation, in Science onForm: Proceedings of the First International Symposium for Science onForm, Y. Kato, R. Takaki and J. Toriwaki , editors, KTK Tokyo, 95-101.

Pandey , R. B., and D. Stauffer (1983) Fractal dimensionality and the number of visited sitesof the ant in the labyrinth, Journal of Physics A, 16, 511-513.

Paterson, L. (1984) Diffusion-limited aggregation and two-fluid displacements in porousmedia, Physical Review Letters, 52(18), 1621-1624.

Pieters, R., and J. S. Langer (1986) Noise-driven sidebranching in the boundary-layer modelof dendritic solidification, Physical Review Letters, 56(18), 1948-1951.

Pfeifer, P. (1984) Fractal dimension as working tool for surface-roughness problems,Applications of Surface Science, 18(1/2), 146-164.

Pfeifer, P., and D. Avnir (1983) Chemistry in noninteger dimensions between two and three.I. Fractal theory of heterogeneous surfaces, Journal of Chemistry and Physics,49(7), 3558-3565.

- 52 -

Pfeifer, P., D. Avnir, and D. Farin (1983) Ideally irregular surfaces, of dimension greater thantwo, in theory and practice, Surface Science, 126(1/3), 569-572.

Racz, Z., and T. Vicsek (1983) Diffusion-controlled deposition: cluster statistics and scaling,Physical Review Letters, 51(26), 2382-2385.

Rudnick, J., and G. Gaspari (1987) The shapes of random walks, Science, 237, 384-388.

Sander, L. M. (1985) Viscous fingers and fractal growth, Nature, 314, 405-406.

Sander, L. M. (1986) Fractal growth processes, Nature, 322, 789-793.

Sander, L. M. (1986) Patterns and disorder in fractal growth processes, in Science onForm: Proceedings of the First International Symposium for Science onForm, Y. Kato, R. Takaki and J. Toriwaki, editors,KTK Scientific, Tokyo, 9-14.

Sander, L. M. (1987) Fractal growth, Scientific American, 256(1), 94-100.

Sawada, Y., A. Dougherty, and J. P. Gollub (1986) Dendritic and fractal patterns inelectrolytic metal deposits, Physical Review Letters, 56(12), 1260-1263.

Schaefer, D. W., J. E. Martin, P. Wiltzius, and D. S. Cannell (1984) Fractal geometry ofcolloidal aggregates, Physical Review Letters, 52(26), 2371-2374.

Schaefer, D. W., and K. D. Keefer (1986) Structure of random porous materials: silicaaerogel, Physical Review Letters, 56(20), 2199-2202.

Schaefer, D. W. (1989) Polymers, fractals and ceramic materials, Science, 243, 1023-1027.

Sherwood, J. D., and J. Nittmann (1986) Gradient governed growth: the effect of viscosityratio on stochastic simulations of the Saffman-Taylor instability, Journal de Physique,47, 15-22.

Stanley, H. E. (1977) Cluster shapes at the percolation threshold: an effective clusterdimensionality and its connection with critical-point exponents, Journal of Physics A,10(11), L211-L220.

Stanley, H. E. (1984) Application of fractal concepts to polymer statistics and to anomaloustransport in randomly porous media, Journal of Statistical Physics, 36(5/6) 843-860.

Stanley, H. E. (1988) Multifractal phenomena in physics and chemistry, Nature, 335, 405-409.

Suzuki, M. (1983) Phase transition and fractals, Progress of Theoretical Physics,69(1), 65-76.

Suzuki, M. (1984) Finite-size scaling for transient similarity and fractals, Progress ofTheoretical Physics, 71(6), 1397-1400.

- 53 -

Takayasu, H., and I. Nishikawa (1986) Directed dendritic fractals, in Science on Form:Proceedings of the First International Symposium for Science on Form, Y.Kato, R. Takaki and J. Toriwaki, editors, KTK Scientific, Tokyo, 15-22.

Tatsumi, J., Y. Kono, and A. Yamauchi (1989) Fractal analysis of plant-root systems,Annals of Biology, 64(5), 499-503.

Termonia, Y., and P. Meakin (1986) Formation of fractal cracks in a kinetic fracture model,Nature, 320, 429-431.

Tomlinson, P. B. (1983) Tree architecture, American Scientist, 71, 141-149.

Turkevich, L. A., and H. Scher (1985) Occupancy-probability scaling in diffusion-limitedaggregation, Physical Review Letters, 55(9), 1026-1029.

Uozumi, J., H. Kimura, and T. Asakura (1990) Optical diffraction by regular and randomKoch fractals, Optics in Complex Systems, Proceedings of SPIE, 1319, Aug. 5-10,Garmisch-Partenkirchen, Germany, 9-10.

Voss, R. F. (1984) Multiparticle fractal aggregation, Journal of Statistical Physics,36(5/6), 861-872.

Weng, J. Q. (1987) The screening behaviour in diffusion-limited aggregation,Communications in Theoretical Physics, 8(1), 113-117.

West, B. J., and A. L. Goldberger (1987) Physiology in fractal dimensions, AmericanScientist, 75, 354-365.

West, B.J., and M. F. Shlesinger (1989) On the ubiquity of 1/f-noise, InternationalJournal of Modern Physics, B3, 795-820.

Winslow, D. N. (1985) The fractal nature of the surface of cement paste, Cement andConcrete Research, 15, 817-824.

Witten, T. A., and M. E. Cates (1986) Tenuous structures from disorderly growth processes,Science, 232, 1607-1612.

Witten, T. A., and L. M. Sander (1981) Diffusion-limited aggregation, a kinetic criticalphenomenon, Physical Review Letters, 47(19), 1400-1403.

Witten, T. A., and L. M. Sander (1983) Diffusion-limited aggregation, Physical ReviewB, 27(9), 5686-5697.